4.6 Article

Gauging anomalous unitary operators

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mechanics

Fermionic quantum cellular automata and generalized matrix-product unitaries

Lorenzo Piroli et al.

Summary: In this paper, the study focuses on matrix-product unitary operators (MPUs) for fermionic one-dimensional chains. A natural generalization of fermionic MPUs is introduced, which preserves locality and is equivalent to fermionic quantum cellular automata (fQCA). An index theorem for generalized MPUs is proven, recovering the classification of fQCA in one dimension.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Article Physics, Multidisciplinary

Symmetry Classes of Open Fermionic Quantum Matter

Alexander Altland et al.

Summary: This study presents a complete symmetry classification of fermion matter in and out of thermal equilibrium, starting from the state transformations in fermionic Fock spaces and the invariance properties of the density matrix dynamical equation. The classification of generators of reversible dynamics, dissipation, and fluctuations in irreversible and interacting dynamical equations leads to a distinction between equilibrium and out-of-equilibrium symmetries, highlighting the role of time in each case. In the context of nonequilibrium quantum dynamics, a novel realization of antilinear symmetries is observed, fundamentally different from the rules of thermal equilibrium.

PHYSICAL REVIEW X (2021)

Article Mathematics

Reflection positivity and invertible topological phases

Daniel S. Freed et al.

Summary: This work implements an extended version of reflection positivity for invertible topological quantum field theories, computes the abelian group of deformation classes using stable homotopy theory, and provides a general formula for symmetry protected topological phases in lattice systems based on field theory considerations. The only inputs required are dimension and symmetry type. Additionally, computations for fermionic systems in physically relevant dimensions are presented, along with discussions on symmetry in quantum field theories and the homotopy theory of relativistic free fermions.

GEOMETRY & TOPOLOGY (2021)

Article Physics, Multidisciplinary

Topological Field Theory of Non-Hermitian Systems

Kohei Kawabata et al.

Summary: This paper develops a field-theoretical description of intrinsic non-Hermitian topological phases, formulated solely in terms of spatial degrees of freedom. The theory provides a universal understanding of non-Hermitian topological phenomena and systematically predicts new physics like transport phenomena and skin effects induced by a perpendicular spatial texture in two dimensions. The non-Hermitian skin effect is shown to be a signature of an anomaly from the field-theoretical perspective.

PHYSICAL REVIEW LETTERS (2021)

Article Physics, Multidisciplinary

Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators

Frederik Nathan et al.

Summary: A new family of few-body topological phases, termed correlation-induced anomalous Floquet insulators (CIAFIs), have been uncovered in periodically driven fermionic systems in two dimensions. These phases are characterized by quantized contributions to bulk magnetization from multi-particle correlations and are classified by integer-valued topological invariants. The study also shows that periodically driven systems of interacting fermions in two dimensions exhibit quantized magnetization in the bulk when fully many-body localized.

SCIPOST PHYSICS (2021)

Article Physics, Multidisciplinary

Effective response theory for Floquet topological systems

Paolo Glorioso et al.

Summary: The effective field theory approach is used to study the topological response of Floquet systems with symmetry group G, introducing a background gauge field suitable for far from equilibrium systems. The response actions serve as many-body topological invariants for topological Floquet unitaries, and new topological response functions are proposed. The response theory captures a symmetry protected version of the chiral unitary index in a particular family of models.

PHYSICAL REVIEW RESEARCH (2021)

Article Materials Science, Multidisciplinary

Classification of interacting Floquet phases with U(1) symmetry in two dimensions

Carolyn Zhang et al.

Summary: In this study, a complete classification of Floquet phases of interacting bosons and fermions with U(1) symmetry in two spatial dimensions was derived, revealing a one-to-one correspondence with rational functions. These rational functions have significant physical meanings related to the stroboscopic edge dynamics of the corresponding systems, such as characterizing the flow of quantum information and U(1) charge at the edge. Additionally, the rational function (pi) over tilde (z) was shown to be directly linked to the time-averaged U(1) current flowing in a specific geometry, serving as a generalization of previously discovered quantized current and magnetization density in noninteracting fermionic Floquet phases.

PHYSICAL REVIEW B (2021)

Article Physics, Mathematical

Classification of Quantum Cellular Automata

Michael Freedman et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2020)

Article Physics, Multidisciplinary

Classification of Matrix-Product Unitaries with Symmetries

Zongping Gong et al.

PHYSICAL REVIEW LETTERS (2020)

Article Physics, Multidisciplinary

Quantum Cellular Automata, Tensor Networks, and Area Laws

Lorenzo Piroli et al.

PHYSICAL REVIEW LETTERS (2020)

Review Physics, Applied

Band structure engineering and non-equilibrium dynamics in Floquet topological insulators

Mark S. Rudner et al.

NATURE REVIEWS PHYSICS (2020)

Article Physics, Multidisciplinary

Observation of Anomalous π Modes in Photonic Floquet Engineering

Qingqing Cheng et al.

PHYSICAL REVIEW LETTERS (2019)

Article Physics, Multidisciplinary

Floquet Chiral Magnetic Effect

Sho Higashikawa et al.

PHYSICAL REVIEW LETTERS (2019)

Review Physics, Condensed Matter

Floquet Engineering of Quantum Materials

Takashi Oka et al.

ANNUAL REVIEW OF CONDENSED MATTER PHYSICS, VOL 10 (2019)

Article Physics, Condensed Matter

Topology and Broken Symmetry in Floquet Systems

Fenner Harper et al.

Annual Review of Condensed Matter Physics (2019)

Article Materials Science, Multidisciplinary

Interacting invariants for Floquet phases of fermions in two dimensions

Lukasz Fidkowski et al.

PHYSICAL REVIEW B (2019)

Article Astronomy & Astrophysics

Supersymmetry breaking and Nambu-Goldstone fermions in interacting Majorana chains

Noriaki Sannomiya et al.

PHYSICAL REVIEW D (2019)

Article Physics, Multidisciplinary

Floquet Supersymmetry

Thomas Iadecola et al.

PHYSICAL REVIEW LETTERS (2018)

Article Physics, Multidisciplinary

Three-Dimensional Chiral Lattice Fermion in Floquet Systems

Xiao-Qi Sun et al.

PHYSICAL REVIEW LETTERS (2018)

Article Materials Science, Multidisciplinary

Matrix product representation of locality preserving unitaries

M. Burak Sahinoglu et al.

PHYSICAL REVIEW B (2018)

Article Materials Science, Multidisciplinary

Many-body spectral reflection symmetry and protected infinite-temperature degeneracy

Michael Schecter et al.

PHYSICAL REVIEW B (2018)

Article Physics, Multidisciplinary

Relationship between symmetry protected topological phases and boundary conformal field theories via the entanglement spectrum

Gil Young Cho et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2017)

Article Mechanics

Matrix product unitaries: structure, symmetries, and topological invariants

J. Ignacio Cirac et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2017)

Article Physics, Multidisciplinary

Quantized Magnetization Density in Periodically Driven Systems

Frederik Nathan et al.

PHYSICAL REVIEW LETTERS (2017)

Article Physics, Multidisciplinary

Floquet Topological Order in Interacting Systems of Bosons and Fermions

Fenner Harper et al.

PHYSICAL REVIEW LETTERS (2017)

Article Physics, Multidisciplinary

Colloquium: Atomic quantum gases in periodically driven optical lattices

Andre Eckardt

REVIEWS OF MODERN PHYSICS (2017)

Article Physics, Particles & Fields

Effective field theory of dissipative fluids

Michael Crossley et al.

JOURNAL OF HIGH ENERGY PHYSICS (2017)

Article Materials Science, Multidisciplinary

Partial time-reversal transformation and entanglement negativity in fermionic systems

Hassan Shapourian et al.

PHYSICAL REVIEW B (2017)

Article Materials Science, Multidisciplinary

Periodic table for Floquet topological insulators

Rahul Roy et al.

PHYSICAL REVIEW B (2017)

Article Materials Science, Multidisciplinary

Floquet topological phases with symmetry in all dimensions

Rahul Roy et al.

PHYSICAL REVIEW B (2017)

Article Physics, Multidisciplinary

All Majorana Models with Translation Symmetry are Supersymmetric

Timothy H. Hsieh et al.

PHYSICAL REVIEW LETTERS (2016)

Article Physics, Multidisciplinary

Classification of topological quantum matter with symmetries

Ching-Kai Chiu et al.

REVIEWS OF MODERN PHYSICS (2016)

Article Multidisciplinary Sciences

Experimental demonstration of anomalous Floquet topological insulator for sound

Yu-Gui Peng et al.

NATURE COMMUNICATIONS (2016)

Article Physics, Multidisciplinary

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

Paraj Titum et al.

PHYSICAL REVIEW X (2016)

Article Physics, Multidisciplinary

Classification of Interacting Topological Floquet Phases in One Dimension

Andrew C. Potter et al.

PHYSICAL REVIEW X (2016)

Article Physics, Multidisciplinary

Chiral Floquet Phases of Many-Body Localized Bosons

Hoi Chun Po et al.

PHYSICAL REVIEW X (2016)

Article Materials Science, Multidisciplinary

Classification of topological phases in periodically driven interacting systems

Dominic V. Else et al.

PHYSICAL REVIEW B (2016)

Article Materials Science, Multidisciplinary

Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

C. W. von Keyserlingk et al.

PHYSICAL REVIEW B (2016)

Article Materials Science, Multidisciplinary

Topological phases protected by reflection symmetry and cross-cap states

Gil Young Cho et al.

PHYSICAL REVIEW B (2015)

Article Materials Science, Multidisciplinary

Thermodynamic equilibrium as a symmetry of the Schwinger-Keldysh action

L. M. Sieberer et al.

PHYSICAL REVIEW B (2015)

Article Physics, Particles & Fields

Fermionic symmetry protected topological phases and cobordisms

Anton Kapustin et al.

JOURNAL OF HIGH ENERGY PHYSICS (2015)

Article Optics

Floquet edge states with ultracold atoms

Matthew D. Reichl et al.

PHYSICAL REVIEW A (2014)

Article Materials Science, Multidisciplinary

Symmetry-protected topological phases, generalized Laughlin argument, and orientifolds

Chang-Tse Hsieh et al.

PHYSICAL REVIEW B (2014)

Article Physics, Multidisciplinary

A new class of (2+1)-dimensional topological superconductors with Z8 topological classification

Xiao-Liang Qi

NEW JOURNAL OF PHYSICS (2013)

Article Materials Science, Multidisciplinary

Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument

Olabode Mayodele Sule et al.

PHYSICAL REVIEW B (2013)

Article Materials Science, Multidisciplinary

Symmetry protected topological orders and the group cohomology of their symmetry group

Xie Chen et al.

PHYSICAL REVIEW B (2013)

Article Physics, Multidisciplinary

Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems

Mark S. Rudner et al.

PHYSICAL REVIEW X (2013)

Article Materials Science, Multidisciplinary

Interacting topological phases and modular invariance

Shinsei Ryu et al.

PHYSICAL REVIEW B (2012)

Article Materials Science, Multidisciplinary

Symmetry protection of topological phases in one-dimensional quantum spin systems

Frank Pollmann et al.

PHYSICAL REVIEW B (2012)

Article Materials Science, Multidisciplinary

Braiding statistics approach to symmetry-protected topological phases

Michael Levin et al.

PHYSICAL REVIEW B (2012)

Article Physics, Multidisciplinary

Order Parameter for Symmetry-Protected Phases in One Dimension

Jutho Haegeman et al.

PHYSICAL REVIEW LETTERS (2012)

Article Physics, Multidisciplinary

Floquet topological insulator in semiconductor quantum wells

Netanel H. Lindner et al.

NATURE PHYSICS (2011)

Article Materials Science, Multidisciplinary

Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations

Xie Chen et al.

PHYSICAL REVIEW B (2011)

Article Materials Science, Multidisciplinary

Classifying quantum phases using matrix product states and projected entangled pair states

Norbert Schuch et al.

PHYSICAL REVIEW B (2011)

Article Materials Science, Multidisciplinary

Classification of gapped symmetric phases in one-dimensional spin systems

Xie Chen et al.

PHYSICAL REVIEW B (2011)

Article Materials Science, Multidisciplinary

Topological phases of fermions in one dimension

Lukasz Fidkowski et al.

PHYSICAL REVIEW B (2011)

Article Physics, Multidisciplinary

Majorana Fermions in Equilibrium and in Driven Cold-Atom Quantum Wires

Liang Jiang et al.

PHYSICAL REVIEW LETTERS (2011)

Article Physics, Multidisciplinary

Topological insulators and superconductors: tenfold way and dimensional hierarchy

Shinsei Ryu et al.

NEW JOURNAL OF PHYSICS (2010)

Article Materials Science, Multidisciplinary

Topological characterization of periodically driven quantum systems

Takuya Kitagawa et al.

PHYSICAL REVIEW B (2010)

Article Materials Science, Multidisciplinary

Photovoltaic Hall effect in graphene

Takashi Oka et al.

PHYSICAL REVIEW B (2009)

Article Materials Science, Multidisciplinary

Topological field theory of time-reversal invariant insulators

Xiao-Liang Qi et al.

PHYSICAL REVIEW B (2008)