| 作者 | J. Fröhlich, A.H. Chamseddine, F. Gabbiani |
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| URL | https://link.springer.com/chapter/10.1007/978-3-0348-9078-6_9 |
| DOI | 10.1007/978-3-0348-9078-6_9. 原文下载 |
| 作者 | Michael Hermele, Matthew P. A. Fisher, and Leon Balents |
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| URL | https://journals.aps.org/prb/abstract/10.1103/PhysRevB.69.064404 |
| 期刊卷码 | Physical Review B, 69卷, 6期, 064404 |
| 日期 | 20 June 2003 |
| DOI | 10.1103/PhysRevLett.106.077003. 原文下载 |
| 摘要 | We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground-state wave function with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped Sz=1/2 spinons carrying the U(1) “electric” gauge charge, a gapped topological point defect or “magnetic” monopole, and a gapless “photon,” which in spin language is a gapless, linearly dispersing Sz=0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as U(1) topological order. This state is stable to all zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wave function. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments. |
| 作者 | Antonino Flachi, Guglielmo Fucci, Muneto Nitta, Satoshi Takada, and Ryosuke Yoshii |
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| URL | https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.085006 |
| 期刊卷码 | Physical Review D, 100卷, 8期, 085006 |
| 日期 | 16 October 2019 |
| DOI | 10.1103/PhysRevD.100.085006. 原文下载 |
| 摘要 | In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional CPN−1 model, restricted to an interval and at finite temperature. We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions, our numerical results show that the ground state has a generic crystal-like structure that can be modulated by variations of the boundary conditions. The results presented here could be relevant for experimental implementations of nonlinear sigma models and could be tested by lattice numerical simulations. |
| 作者 | Jongmin Han |
|---|---|
| URL | http://hdl.handle.net/2433/194921. 原文下载 |
| 期刊卷码 | 数理解析研究所講究録 (2013), 1837: 29-43 |
| 日期 | 2013-06 |
| 摘要 | In this paper, we survey recent progress for the study of partial differential equations arising from the self-dual Chern-Simons gauged $O(3)$ sigma model. We review the classical O(3) sigma model and its extension to gauge field models. Especially, the Maxwell gauged model and the Chern-Simons gauged models are described for broken and unbroken symmetries. We derive the self-dual equations and their reduction to the elliptic equations. We discuss recent progress for the existence of solutions for the reduced equations. |
| 作者 | Max A. Metlitski and Ashvin Vishwanath |
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| URL | https://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.245151 |
| 期刊卷码 | Physical Review B, 93卷, 24期, 245151 |
| 日期 | 27 June 2016 |
| DOI | 10.1103/PhysRevB.93.245151. 原文下载 |
| 摘要 | Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here, we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by a dual theory, QED3, with again a single Dirac fermion but coupled to a gauge field. This duality is established by considering two alternate descriptions of the three-dimensional topological insulator (TI) surface. The first description is the usual Dirac fermion surface state. The dual description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, which maps it to a gauged chiral topological insulator. This alternate description ultimately leads to a new surface theory, QED3, which provides a simple description of otherwise intractable interacting electronic states. For example, an explicit derivation of the T-Pfaffian state, a proposed surface topological order of the TI, is obtained by simply pair condensing the dual fermions. The roles of time-reversal and particle-hole symmetries are exchanged by the duality, which connects some of our results to a recent conjecture by Son on particle-hole symmetric quantum Hall states. |
| 作者 | A J Beekman, D Sadri and J Zaanen |
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| URL | https://iopscience.iop.org/article/10.1088/1367-2630/13/3/033004 |
| 期刊卷码 | New Journal of Physics, 13卷, 3期, 033004 |
| 日期 | 2 March 2011 |
| DOI | 10.1088/1367-2630/13/3/033004. 原文下载 |
| 摘要 | Dualities yield considerable insight into field theories by relating the weak coupling regime of one theory to the strong coupling regime of another. A prominent example is the 'vortex–boson' (or 'Abelian-Higgs', 'XY') duality in 2+1 dimensions demonstrating that the quantum disordered superfluid is equivalent to an ordered superconductor and the other way around. Such a duality structure should be ubiquitous, but despite the simplicity of the complex scalar field theory in 3+1 (and higher) dimensions, a precise formulation of the duality is lacking. In 2+1 dimensions the construction rests on the fact that the topological excitations of the superfluid (vortices) are particle-like and the dual superconductor corresponds just to a conventional Bose condensate of vortices. Departing from the superfluid, the vortices in 3+1d are Nielsen–Olesen strings and the difficulty is in the construction of string field theory. We demonstrate that an earlier attempt [1] to construct the dual theory is subtly flawed. Relying on the understanding of the physics of the disordered superfluid in higher dimensions, as well as a gauge invariant formulation of the Higgs mechanism at work in this context, we derive the effective action for the dual string superconductor in 3+1d. This turns out to be a very simple affair: the string condensate just supports a massive compressional mode, while it gives mass to the 2-form transversal photon that represents the remnant of the zero sound mode of the superfluid. We conclude with the observation that the 2+1d superfluid–superconductor duality actually persists in all D+1 dimensions with D ≥ 2: the condensates are formed from D − 2-branes interacting via D − 1-form gauge fields but the form of the effective theory of the dual superconductor is eventually independent of dimensionality. Finally, we demonstrate that Bose–Mott insulators support topological defects that are string-like in 3+1d. This surprising implication of duality may be seen in cold atom experiments. |
| 作者 | Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang | |
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| URL | https://journals.aps.org/prb/abstract/10.1103/PhysRevB.78.195424 | Erratumhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.81.159901 |
| 期刊卷码 | Physical Review B, 78卷, 19期, 195424 | Erratum Physical Review B, 81卷, 15期, 159901 |
| 日期 | 24 November 2008 | Erratum 6 April 2010 |
| DOI | 10.1103/PhysRevB.78.195424. 原文下载 | Erratum10.1103/PhysRevB.81.159901. 原文下载 |
| 摘要 | We show that the fundamental time-reversal invariant (TRI) insulator exists in 4+1 dimensions, where the effective-field theory is described by the (4+1)-dimensional Chern-Simons theory and the topological properties of the electronic structure are classified by the second Chern number. These topological properties are the natural generalizations of the time reversal-breaking quantum Hall insulator in 2+1 dimensions. The TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimensions can be obtained as descendants from the fundamental TRI insulator in 4+1 dimensions through a dimensional reduction procedure. The effective topological field theory and the Z2 topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of measurable phenomena, the most striking of which is the topological magnetoelectric effect, where an electric field generates a topological contribution to the magnetization in the same direction, with a universal constant of proportionality quantized in odd multiples of the fine-structure constant α=e2/hc. Finally, we present a general classification of all topological insulators in various dimensions and describe them in terms of a unified topological Chern-Simons field theory in phase space. |
| 作者 | Edward Witten |
|---|---|
| URL | https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.88.035001 |
| 期刊卷码 | Reviews of Modern Physics, 88卷, 3期, 035001 |
| 日期 | 13 July 2016 |
| DOI | 10.1103/RevModPhys.88.035001. 原文下载 |
| 摘要 | Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here a description is given in detail of what this picture means for phases of quantum matter that can be understood via band theory and free fermions. The main examples considered are time-reversal invariant topological insulators and superconductors in two or three space dimensions. Along the way, the precise meaning of the statement that in the bulk of a 3D topological insulator, the electromagnetic θ angle is equal to π, is clarified. |
| 作者 | Ferdinand Evers and Alexander D. Mirlin |
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| 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 | Irina Aref'eva, Mikhail Khramtsov, Maria Tikhanovskaya, and Igor Volovich |
|---|---|
| URL | https://arxiv.org/abs/1811.04831 |
| DOI | 10.1007/JHEP07(2019)113. 原文下载 |
| 摘要 | We study the SYK model in the large N limit beyond the replica-diagonal approximation. First we show that there are exact replica-nondiagonal solutions of the saddle point equations for q=2 for any finite replica number M. In the interacting q=4 case we are able to construct the numerical solutions, which are in one-to-one correspondence to the analytic solutions of the quadratic model. These solutions are singular in the M→0 limit in both quadratic and quartic interaction cases. The calculations of the on-shell action at finite integer M show that the nondiagonal replica-symmetric saddles are subleading in both quadratic and quartic cases. We also study replica-nondiagonal solutions of the SYK in the strong coupling limit. For arbitrary q we show that besides the usual solutions of the replica-diagonal saddle point equations in the conformal limit, there are also replica-nondiagonal solutions for any value of M (including zero). The specific configurations that we study, have factorized time and replica dependencies. The corresponding saddle point equations are separable at strong coupling, and can be solved using the Parisi ansatz from spin glass theory. We construct the solutions which correspond to the replica-symmetric case and to one-step replica symmetry breaking. We compute the regularized free energy on these solutions in the limit of zero replicas. It is observed that there are nondiagonal solutions with the regularized free energy lower than that of the standard diagonal conformal solution. |