| 作者 | Jorge V. José, Leo P. Kadanoff, Scott Kirkpatrick, and David R. Nelson | |
|---|---|---|
| URL | https://journals.aps.org/prb/abstract/10.1103/PhysRevB.16.1217 | Erratumhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.81.159901 |
| 期刊卷码 | Physical Review B, 16卷, 3期, 1217 | Erratum Physical Review B, 17卷, 3期, 1477 |
| 日期 | 1 August 1977 | Erratum 1 February 1978 |
| DOI | 10.1103/PhysRevB.16.1217. 原文下载 | Erratum10.1103/PhysRevB.17.1477. 原文下载 |
| 摘要 | The classical planar Heisenberg model is studied at low temperatures by means of renormalization theory and a series of exact transformations. A numerical study of the Migdal recursion relation suggests that models with short-range isotropic interactions rapidly become equivalent to a simplified model system proposed by Villain. A series of exact transformations then allows us to treat the Villain model analytically at low temperatures. To lowest order in a parameter which becomes exponentially small with decreasing temperature, we reproduce results obtained previously by Kosterlitz. We also examine the effect of symmetry-breaking crystalline fields on the isotropic planar model. A numerical study of the Migdal recursion scheme suggests that these fields (which must occur in real quasi-two-dimensional crystals) are strongly relevant variables, leading to critical behavior distinct from that found for the planar model. However, a more exact low-temperature treatment of the Villain model shows that hexagonal crystalline fields eventually become irrelevant at temperatures below the Tc of the isotropic model. Isotropic planar critical behavior should be experimentally accessible in this case. Nonuniversal behavior may result if cubic crystalline fields dominate the symmetry breaking. Interesting duality transformations, which aid in the analysis of symmetry-breaking fields are also discussed. |
| 作者 | Senthil Todadri |
|---|---|
| URL | https://ui.adsabs.harvard.edu/abs/1997PhDT.......192T/abstract. 原文下载 |
| 日期 | 1997-12 |
| 摘要 | A number of condensed matter systems undergo a phase transition at zero temperature as some external parameter (such as pressure, magnetic field, or amount of dirt) is varied. Quantum effects are often crucial to the physics of this phenomenon hence the name "quantum phase transitions". This thesis is concerned with a study of such zero temperature phase transitions in the presence of static randomness (due to impurities or other frozen defects in the system). Experimentally accessible quantum phase transitions often occur in the presence of strong randomness, and are very poorly understood. Theoretically, the description of such phenomena involving competition between various kinds of potential energy of interactions, quantum effects, and randomness presents a challenging problem, where there are as yet few reliable techniques. This thesis studies simple quantum statistical models with randomness as a useful starting point to obtain insight into more complex, realistic systems. Progress is reported in understanding various simple but non-trivial models of random quantum magnetic systems in the vicinity of a quantum phase transition. The results show that the effects of randomness may be quite dramatic, and lead to a phenomenology that is strikingly different from that of pure systems. |
| 作者 | Kenneth G.Wilson and J.Kogut |
|---|---|
| URL | https://www.sciencedirect.com/science/article/abs/pii/0370157374900234#:~:text=Kogut%2C%20The%20renormalization%20group%20and%20the%20e%20expansion,the%20values%20of%20p%28x%29%20at%20macroscopically%20separated%20points. |
| 期刊卷码 | Physics Reports, 12卷, 2期, 75 |
| 日期 | August 1974 |
| DOI | 10.1016/0370-1573(74)90023-4. 原文下载 |
| 摘要 | The modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory. The expansion in ϵ = 4−d is explained [d is the dimension of space (statistical mechanics) or space-time (quantum field theory)]. The emphasis is on principles, not particular applications. Sections 1–8 provide a self-contained introduction at a fairly elementary level to the statistical mechanical theory. No background is required except for some prior experience with diagrams. In particular, a diagrammatic approximation to an exact renormalization group equation is presented in sections 4 and 5; sections 6–8 include the approximate renormalization group recursion formula and the Feyman graph method for calculating exponents. Sections 10–13 go deeper into renormalization group theory (section 9 presents a calculation of anomalous dimensions). The equivalence of quantum field theory and classical statistical mechanics near the critical point is established in section 10; sections 11–13 concern problems common to both subjects. Specific field theoretic references assume some background in quantum field theory. An exact renormalization group equation is presented in section 11; sections 12 and 13 concern fundamental topological questions. |
| 作者 | Stephen Christopher Powell |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2007 |
| 摘要 | In recent years, new advances in techniques for trapping and cooling atoms have allowed the production of atomic gases at low-enough temperatures and high-enough
densities for collective quantum-mechanical effects to become important. This thesis describes theoretical investigations of certain many-body physics problems motivated
by these experimental developments. It consists of two main parts.
In the first, I investigate the array of phases exhibited by degenerate mixtures of bosons and fermions with a Feshbach resonance, a bound molecular state whose energy can be tuned with a magnetic field. These phases are distinguished by the presence or absence of a bosonic condensate and also by the different Luttinger constraints that are shown to apply to the Fermi surface(s). The second part is concerned with bosons in an optical lattice, in which a periodic potential is produced by counterpropagating lasers. Spinless bosons are known to exhibit a quantum phase transition between a Mott insulator and a superfluid state, while bosons with spin have a much richer phase structure. I consider, in particular, a phase transition with a spinless order parameter, and show that the long-time dynamics of spin-carrying excitations is governed by a nontrivial fixed point. The corresponding anomalous exponents are found using a renormalization-group calculation. |
| 作者 | Jason Iaconis |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2012 |
| 摘要 | In this thesis we take several different analytic and numerical approaches to studying the classical J-K model. This model describes an interacting many-body system of spins with continuous symmetry which interact via 2-site nearest-neighbour exchange terms and 4-site ring-exchange terms. We begin by looking at the traditional solution of the XY model, in order to gain insight into the behaviour and general properties of the system. Classical Monte Carlo simulations will then be used to study the properties of the J-K model in different regimes of phase space. We will see that we can use properties from the theoretical solution of the XY model to study the Kosterlitz-Thouless phase transition numerically. We then extend our simulation to study the aspect ratio scaling of the superfluid density in the XY model. It will also be shown that there exists a finite temperature phase transition in the pure-K ring-exchange model. After this we will develop a mapping from the 1D quantum Bose-Hubbard model to the 2D J-K model and use this mapping to search for topological phases in classical Hamiltonians. However, we find that our mapping fails to reproduce the topological phase present in the quantum model. Finally we will look at the XY model using tools from information theory. A method for measuring mutual information in classical Monte Carlo simulations is developed. We then show that this measurement of mutual information can be used as a completely new way to identify the Kosterlitz-Thouless phase transition in Monte Carlo simulations. |
| 作者 | Hsin-Hua Lai |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2012 |
| 摘要 | The recent experimental realizations of spin-1/2 gapless quantum spin liquids in twodimensional triangular lattice organic compounds EtMe3Sb[Pd(dmit)2]2 and κ-(ET)2Cu2(CN)3 have stimulated the investigation of the gapless spin liquid theories. The models in dimensions greater than one (D > 1) usually involve multispin interactions, such as ring exchange interactions, that are difficult to study, while effective gauge theory descriptions are not well-controlled to give reliable physics information. Driven by the need for a systematic and controlled analysis of such phase, such models on ladders are seriously studied. This thesis first focuses on such ladder models. We propose that the gapless spin liquid phase can be accessed from a two-band interacting electron model by metal-Mott insulator phase transition. We use Bosonization analysis and weak-coupling Renormalization Group to further study the gapless spin liquid state in the presence of Zeeman magnetic fields or orbital magnetic fields. Several new exotic gapless spin liquids with dominant spin nematic correlations are predicted. In such a ladder spin liquid, we also consider the impurity effects. We conclude that the local energy textures and oscillating spin susceptibilities around the impurities are nontrivial and can be observed in the experiments. We then shift our focus to another theoretical candidate, an SU(2)-invariant spin liquid with Majorana excitations, which can also qualitatively explain the experimental phenomenology. We construct an exactly solvable Kitaev-type model realizing the long-wavelength Majorana spin liquid state and study its properties. We find that the state has equal power-law spin and spin-nematic correlations and behaves nontrivially in the presence of Zeeman magnetic fields. Finally, we realize such Majorana spin liquid states on a two-leg ladder and further explore their stability. We conclude the states can be stable against short-range interactions and gauge field fluctuations. |
| 作者 | Benjamin F. McKeever |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2016 |
| 摘要 | Quantum dot devices may be tuned to Kondo models which each have a non-interacting limit called the Toulouse limit. At sufficiently low temperatures the Toulouse limit can be used to make predictions for charge transport in such devices driven away from equilibrium, e.g. with an ac bias. We investigate non-equilibrium transport in a resonant level model with a single lead which may be mapped onto the Toulouse limit of the Kondo model. The main results are expressions for the charge current that are exact in the tunnelling couplings, while remaining in the linear response regime of the time-dependent voltage bias. We also show how the line of enquiry directly extends to the tunnelling junction studied by A. Schiller and S. Hershfield in which a Kondo impurity interacts separately with two leads. |
| 作者 | Sam Eigenhuis |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2016 |
| 摘要 | It is well known that dissipation usually induces decoherence in quantum systems. However, recently it has been employed to engineer zero-energy Majorana modes on the boundary of a one-dimensional fermionic chain by using the Lindblad master equation [1]. In this thesis, by employing the Caldeira-Leggett theory of quantum dissipation, we study the equivalence between a particle on a one-dimensional lattice coupled to a thermal bath, and the massless Luttinger liquid with an impurity on the boundary in a closed system [2–4]. In particular, the Luttinger liquid with a single impurity at the boundary of a semi-infinite chain is bosonized into the boundary sine-Gordon theory. Here, a zero-energy Majorana mode appears at the boundary when the Luttinger parameter K = 1/2. The equivalence is shown to apply also in the case of helical Luttinger liquids, which play an important role in topological insulators. This equivalence is then generalized to the full sine-Gordon theory, such that massive Luttinger liquids can be mapped to a single-particle one-dimensional tunneling Hamiltonian with a dissipative Ohmic Caldeira-Leggett bath. |
| 作者 | Sambuddha Sanyal |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2013 |
| 摘要 | In this thesis we have studied four different problems on the effects of disorders in low dimensional quantum systems. In the first problem we studied the how the low energy properties of a non-interacting system of electron on a bipartite lattice gets effected due to random site dilution. We conclude that the behavior of the density of states the gapless phase is of so called “Gade type” and in the gapped phase is of so called “Griffiths” type. We also tried to understand the possible origin of generation of such states at low energy. In the second problem we have tried to understand the effect of random site dilution in a SU(2) symmetric spin model by mapping the model into a non interacting fermion gas, this map helped us to understand the behavior of the spin system from the results of the non-interacting electronic systems of previous problem. We conclude that from the magnetic response of the system that at low energy the system stabilizes to a “random-singlet” phase. In the third problem we have focused on the ground state properties of finite size antiferromagnetic which can arise in a thermodynamic system as a result of random site dilution. In the fourth problem we focused on the effects of a single impurity on the spin texture in an antiferromagnetically ordered spin chain. |
| 作者 | D J Amit, Y Y Goldschmidt and S Grinstein |
|---|---|
| URL | https://iopscience.iop.org/article/10.1088/0305-4470/13/2/024 |
| 期刊卷码 | Journal of Physics A: Mathematical and General, 13卷, 2期, 585 |
| 日期 | 19 July 1979 |
| DOI | 10.1088/0305-4470/13/2/024. 原文下载 |
| 摘要 | A systematic renormalisation group technique for studying the 2D sine-Gordon theory (Coulomb gas, XY model) near its phase transition is presented. The new results are (a) higher order terms in the flow equations beyond those of Kosterlitz (1974) give rise to a new universal quantity; (b) this in turn gives the universal form as well as the relative coefficient of the next-to-leading term in the correlation function of the XY model; (c) the free energy (1PI vacuum sum) is calculated after the singularity at beta 2=4 pi is treated; (d) vortices with multiple charges are shown to be irrelevant; (e) symmetry breaking fields are analysed systematically. The main ideas that the sine-Gordon theory can be defined as a double expansion in alpha (fugacity) and delta = beta 2/8 pi -1 (distance from the critical temperature at alpha =0). Wave-function and coupling constant ( alpha ) renormalisations are necessary and sufficient, around beta 2=8 pi where cos phi acquires dimension 2, for functions with elementary SG fields. This gives rise to renormalisation of beta . The renormalisability is proved to the order calculated in the context of the SG theory, and in general, by using the equivalence to the Thirring-Schwinger model. The renormalised beta 2 plays a role analogous to the dimension in a phi 4 theory-8 pi being the critical dimension. beta 2>8 pi gives an infrared asymptotically free theory which leads to the well-known fixed line. The infrared properties are understood by analogy with the non-linear sigma model. |
| 作者 | DUNG-HAI LEE and MATTHEW P.A. FISHER |
|---|---|
| URL | https://www.worldscientific.com/doi/abs/10.1142/S0217979291001061 |
| 期刊卷码 | International Journal of Modern Physics B, 05卷, 16 & 17期, 2675 |
| DOI | 10.1142/S0217979291001061. 原文下载 |
| 摘要 | We review recent work on a bosonic formulation of both anyon superconductivity and the fractional quantum Hall effect (FQHE). Central to this approach is the concept of charge-vortex duality in two-dimensional (2d) boson systems. A formal duality transformation which takes one from a particle to a vortex representation of a 2d boson model is described in detail. The duality transformation is employed to obtain detailed properties of both the FQHE hierarchy and a hierarchy of anyon superconducting phases. |
| 作者 | Lorenz Eberhardt, ETH Zürich |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | February 19, 2019 |
| 摘要 | We introduce the principal chiral model in two dimensions and its extension by the Wess-Zumino term. We discuss the symmetries, corresponding currents and their quantum algebra. We explain the Sugawara construction to demonstrate that the Wess-Zumino-Witten model defines a conformal field theory. We then move on and discuss representations, characters, fusion and modular invariants by following the example of su(2). Finally, we briefly discuss the coset construction. |
| 作者 | Igor Boettcher, Jan M. Pawlowski and Sebastian Diehl |
|---|---|
| URL | https://www.sciencedirect.com/science/article/pii/S0920563212001612?via%3Dihub |
| 期刊卷码 | Nuclear Physics B - Proceedings Supplements, 228卷, 63 |
| DOI | 10.1016/j.nuclphysbps.2012.06.004. 原文下载 |
| 摘要 | We give a self-contained introduction to the physics of ultracold atoms using functional integral techniques. Based on a consideration of the relevant length scales, we derive the universal effective low energy Hamiltonian describing
ultracold alkali atoms. We then introduce the concept of the effective action, which generalizes the classical action principle to full quantum status and provides an intuitive and versatile tool for practical calculations. This framework
is applied to weakly interacting degenerate bosons and fermions in the spatial continuum. In particular, we discuss the related BEC and BCS quantum condensation mechanisms. We then turn to the BCS-BEC crossover, which interpolates between
both phenomena, and which is realized experimentally in the vicinity of a Feshbach resonance. For its description, we introduce the Functional Renormalization Group approach. After a general discussion of the method in the cold atoms context,
we present a detailed and pedagogical application to the crossover problem. This not only provides the physical mechanism underlying this phenomenon. More generally, it also reveals how the renormalization group can be used as a tool to
capture physics at all scales, from few-body scattering on microscopic scales, through the finite temperature phase diagram governed by many-body length scales, up to critical phenomena dictating long distance physics at the phase transition.
The presentation aims to equip students at the beginning PhD level with knowledge on key physical phenomena and flexible tools for their description, and should enable to embark upon practical calculations in this field. |
| 作者 | Kenneth Halpern |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 1996 |
| 摘要 | We employ Wilson's renormalization group procedure in an attempt to classify and understand the physics of the continuum limits of scalar field theories. Analysis of the flows near the Gaussian fixed point reveals the existence of an infinite set of asymptotically free continuum limits. We study the associated physics by calculating scattering cross sections and the i-loop effective potential. Examination of the latter provides evidence for the existence of a phase boundary in parameter space between those theories with broken symmetry and those with unbroken symmetry. We extend the flow analysis near the Gaussian fixed point to Bose/Fermi theories possessing arbitrary internal symmetries. Fermionic interactions are found to decouple in parameter space. The behavior of renormalization group trajectories near the Gaussian fixed point is solely determined by the Bosonic structure of the theory. |
| 作者 | Archishman Raju |
|---|---|
| 原文下载 | 原文下载 |
| 日期 | 2018 |
| 摘要 | The main part of this thesis is on the renormalization group (RG). We will explore the results of the RG in two ways. In the first part we use information geometry, in which the local distance between models measures their distinguishability from data, to quantify the flow of information under the renormalization group. We show that information about relevant parameters is preserved, with distances along relevant directions maintained under flow. By contrast, irrelevant parameters become less distinguishable under the flow, with distances along irrelevant directions contracting according to renormalization group exponents. We develop a covariant formalism to understand the contraction of the model manifold. We then apply our tools to understand the emergence of the diffusion equation and more general statistical systems described by a free energy. Our results give an informationtheoretic justification of universality in terms of the flow of the model manifold under coarse graining. In the second part, we use dynamical systems theory to systematize the results of the RG. The results of the RG are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a case-by-case basis. We use the mathematics of normal form theory to systematically group these into universality families of seemingly unrelated systems united by common scaling variables. We recover and explain the existing literature, predict the nonlinear generalization for universal homogeneous functions, and show that the procedure leads to a better handling of the singularity with several examples including the Random Field Ising model and the 4-d Ising model. The RG is useful not just for systems in physics but has found application in a surprising variety of fields. In dynamical systems, it provided an nice explanation of the universality observed in the period doubling transition. We show the equivalent of so-called redundant variables in period doubling and offer a new interpretation for them. We then examine the consequences for the Ising model. Finally, the last part of this thesis is on a very different topic. Here, we use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the resonances, the dynamics typically has a finite region in phase space where it is stable. Inherent noise in the system leads to particle loss from this stable region. The competition of this noise with radiation damping, which increases stability, determines the escape rate. Determining this ‘aperture’ and finding escape rates is therefore an important physical problem. We compare the results of two different perturbation theories and a variational method to estimate this stable region. Including noise, we derive analytical estimates for the steady-state populations (and the resulting beam emittance), for the escape rate in the small damping regime, and compare them with numerical simulations. |
| 作者 | Andreas W. W. Ludwig, Matthew P. A. Fisher, R. Shankar, and G. Grinstein |
|---|---|
| URL | https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.7526 |
| 期刊卷码 | Physical Review B, 50卷, 11期, 7526 |
| 日期 | 15 September 1994 |
| DOI | 10.1103/PhysRevB.50.7526. 原文下载 |
| 摘要 | We introduce and analyze a class of model systems to study transitions in the integer quantum Hall effect (IQHE). Even without disorder our model exhibits an IQHE transition as a control parameter is varied. We find that the transition is in the two-dimensional Ising universality class and compute all associated exponents and critical transport properties. The fixed point has time-reversal, particle-hole, and parity invariance. We then consider the effect of quenched disorder on the IQHE transition and find the following. (i) Randomness in the control parameter (which breaks all the above symmetries) translates into bond randomness in the Ising model and is hence marginally irrelevant. The transition may equally well be viewed as a quantum percolation of edge states localized on equipotentials. The absence of random-phase factors for the edge states is responsible for the nongeneric (Ising) critical properties. (ii) For a random magnetic field (which preserves particle-hole symmetry in every realization) the model exhibits an exactly solvable fixed line, described in terms of a product of a Luttinger liquid and an SU(n) spin chain. While exponents vary continuously along the fixed line, the longitudinal conductivity is constant due to a general conformal sum rule for Kac-Moody algebras (derived here), and is computed exactly. We also obtain a closed expression for the extended zero-energy wave function for every realization of disorder and compute its exact multifractal spectrum f(α) and the exponents of all participation ratios. One point on the fixed line corresponds to a recently proposed model by Gade and Wegner. (iii) The model in the presence of a random on-site potential scales to a strong disorder regime, which is argued to be described by a symplectic nonlinear-sigma-model fixed point. (iv) We find a plausible global phase diagram in which all forms of disorder are simultaneously considered. In this generic case, the presence of random-phase factors in the edge-state description indicates that the transition is described by a Chalker-Coddington model, with a so far analytically inaccessible fixed point. |
| 作者 | Gennady Y. Chitov and David Sénéchal |
|---|---|
| URL | https://journals.aps.org/prb/abstract/10.1103/PhysRevB.57.1444 |
| 期刊卷码 | Physical Review B, 57卷, 3期, 1444 |
| 日期 | 15 January 1998 |
| DOI | 10.1103/PhysRevB.57.1444. 原文下载 |
| 摘要 | We apply the finite-temperature renormalization group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation-invariant Fermi surface. The basic quantities of Fermi-liquid theory, the Landau function, and the scattering vertex are calculated as fixed points of the RG flow in terms of the effective action’s interaction function. The classic derivations of Fermi-liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi-liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid. |
| 作者 | Somendra M. Bhattacharjee |
|---|---|
| 日期 | October 4, 2018 |
| 原文下载 | 原文下载 |
| 摘要 | The effects of two types of randomness on the behaviour of directed polymers are discussed in this chapter. The first part deals with the effect of randomness in medium so that a directed polymer feels a random external potential. The second part deals with the RANI model of two directed polymers with heterogeneity along the chain such that the interaction is random. The random medium problem is better understood compared to the RANI model. |
| 作者 | Robert Savit |
|---|---|
| URL | https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.52.453 |
| 期刊卷码 | Reviews of Modern Physics, 52卷, 2期, 453 |
| 日期 | 20 June 2003 |
| DOI | 10.1103/RevModPhys.52.453. 原文下载 |
| 摘要 | This paper presents a pedagogical review of duality (in the sense of Kramers and Wannier) and its application to a wide range of field theories and statistical systems. Most of the article discusses systems in arbitrary dimensions with discrete or continuous Abelian symmetry. Globally and locally symmetric interactions are treated on an equal footing. For convenience, most of the theories are formulated on a d-dimensional (Euclidean) lattice, although duality transformations in the continuum are briefly described. Among the familiar theories considered are the Ising model, the x−y model, the vector Potts model, and the Wilson lattice gauge theory with a ZN or U(1) symmetry, all in various dimensions. These theories are all members of a more general heirarchy of theories with interactions which are distinguished by their geometrical character. For all these Abelian theories it is shown that the duality transformation maps the high-temperature (or, for a field theory, large coupling constant) region of the theory into the low-temperature (small coupling constant) region of the dual theory, and vice versa. The interpretation of the dual variables as disorder parameters is discussed. The formulation of the theories in terms of their topological excitations is presented, and the role of these excitations in determining the phase structure of the theories is explained. Among the other topics discussed are duality for the Abelian Higgs model and related models, duality transformations applied to random systems (such as theories of a spin glass), duality transformations in the "lattice Hamiltonian" formalism, and a description of attempts to construct duality transformations for theories with a non-Abelian symmetry, both on the lattice and in the continuum. |
| 作者 | A. M. Chang |
|---|---|
| URL | https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.1449 |
| 期刊卷码 | Reviews of Modern Physics, 75卷, 4期, 1449 |
| 日期 | 13 November 2003 |
| DOI | 10.1103/RevModPhys.75.1449. 原文下载 |
| 摘要 | The edges of quantum Hall fluids behave as one-dimensional conductors. This article reviews electron transport into these edge states, covering both the theory based on the chiral Luttinger liquid and the experimental findings using electron tunneling as the probe. The first part of the review presents a basic description of this theory, including a derivation of the density of states, to provide a framework and language for discussing the experimental observations. The signature of the chiral Luttinger liquid is a power-law behavior for the density of states and the tunneling conductances. Experimentally, two techniques have been applied to study the tunneling conductance, using a gated point contact between two quantum Hall edges, or using a cleaved-edge barrier between an edge and a normal conductor. The point-contact method exhibits resonant tunneling, which appears to show some aspects of the Luttinger liquid, and the cleaved-edge method has yielded clear power-law dependences in the off-resonance conductances. Power-law behavior over many orders of magnitude is observed, confirming the Luttinger-liquid character of the edge states. However, the power-law exponents, while in agreement with finite-size numerical calculations, can differ from the universal values predicted by the Chern-Simon field theory. This disagreement is still not well understood. The review concludes with a brief survey of other one-dimensional conductors that have been studied to look for characteristics of the nonchiral Tomonaga-Luttinger liquid. |
| 作者 | Ferdinand Evers and Alexander D. Mirlin |
|---|---|
| URL | https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.80.1355 |
| 期刊卷码 | Reviews of Modern Physics, 80卷, 4期, 1355 |
| 日期 | 17 October 2008 |
| DOI | 10.1103/RevModPhys.80.1355. 原文下载 |
| 摘要 | The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term “Anderson transition” is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations. |
| 作者 | A. M. Polyakov |
|---|---|
| 原文下载 | 原文下载 |