Topological Phase Transition

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18:27 Editors' SuggestionsCrystalline topological phases as defect networks

Author(s): Dominic V. Else and Ryan Thorngren In order to understand topological phases of matter that exist in crystalline solids, it is necessary to take into account their spatial symmetries, which gives a notion of crystalline topological phases. Here, the authors give a general picture for understanding such phases. The idea is that ground states in such phases can be schematically represented by a crystalline network of defects imprinted on a topological substrate. Equivalence classes of such defect networks under symmetric deformations correspond precisely to crystalline topological phases.
[Phys. Rev. B 99, 115116] Published Thu Mar 14, 2019

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17:06 Editors' SuggestionsMultiple topological transitions in twisted bilayer graphene near the first magic angle

Author(s): Kasra Hejazi, Chunxiao Liu, Hassan Shapourian, Xiao Chen, and Leon Balents The noninteracting physics of electrons in twisted bilayer graphene is considered by varying the twist angle close to the magic angle using a continuum model. The magic angle is known to occur when the dispersion at the two Dirac cones of the two bands close to neutrality become quadratic. These are topological transitions, in which three moving Dirac points pass through each of the two immobile ones as the angle varies. Indeed, the motion of Dirac points is not limited to this and their participation in several topological transitions is very rich, which is the main subject of this study.
[Phys. Rev. B 99, 035111] Published Mon Jan 07, 2019

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17:05 Editors' SuggestionsHigher-order topological phases: A general principle of construction

Author(s): Dumitru Călugăru, Vladimir Juričić, and Bitan Roy The surface states of a d-dimensional conventional or first-order topological state of matter reside on a (d-1) dimensional boundary. However, its nth order incarnation, commonly known as a higher-order topological (HOT) phase, accommodates (d-n) dimensional boundary states, with corner and hinge modes standing as their representatives. Here, the authors introduce a general principle of systematically constructing the hierarchy of HOT phases by exploiting the symmetry of the system and the corresponding Clifford algebra. This procedure is applicable for insulating as well as gapless phases, and paves the route toward realizing a fourth-order nodal-loop semimetal, devoid of any surface bound state.
[Phys. Rev. B 99, 041301(R)] Published Fri Jan 04, 2019

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19:28 Nature.ComElectric-field-tuned topological phase transition in ultrathin Na

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18:10 Editors' SuggestionsParadoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system

Author(s): Denis R. Candido, Maxim Kharitonov, J. Carlos Egues, and Ewelina M. Hankiewicz In quantum anomalous Hall systems (Chern insulators) the topological Chern number defines, via bulk-boundary correspondence, the number of the edge-state bands that connect the valence and conduction bulk bands. This is the only characteristic of the edge states required by quantum Hall topology. Here, the authors present a paradoxical finding that, in the vicinity of a topological phase transition in a quantum anomalous Hall system, topology nearly always results in a significant extension of the edge-state structure beyond the minimal one required to satisfy the Chern numbers.
[Phys. Rev. B 98, 161111(R)] Published Mon Oct 15, 2018

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18:04 Editors' SuggestionsAvoided level crossing at the magnetic field induced topological phase transition due to spin-orbital mixing

Author(s): G. Krizman, B. A. Assaf, M. Orlita, T. Phuphachong, G. Bauer, G. Springholz, G. Bastard, R. Ferreira, L. A. de Vaulchier, and Y. Guldner A three-dimensional gapless Dirac state is expected to occur at the critical point between a topological and a trivial phase. By applying a strong magnetic field or increasing temperature, a transition from topological to trivial can be induced in the topological crystalline insulator Pb1−xSnxSe (x>0.16). Using magneto-optical spectroscopy, the authors show that the critical gapless Dirac state is unstable in the case of Pb1−xSnxSe (x=0.19). An avoided crossing of energy bands is observed when a topological phase transition is induced by a magnetic field or by increasing temperature. The avoided crossing is accompanied by a spin-orbital mixing of the band-edge parity. These results motivate

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18:14 Editors' SuggestionsTopological Phases of Non-Hermitian Systems

Author(s): Zongping Gong, Yuto Ashida, Kohei Kawabata, Kazuaki Takasan, Sho Higashikawa, and Masahito Ueda A new theoretical framework for topological phases provides the first systematic classification of non-Hermitian systems, those that exchange matter and energy with their environment.
[Phys. Rev. X 8, 031079] Published Mon Sep 24, 2018

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19:09 Editors' SuggestionsDyonic Lieb-Schultz-Mattis theorem and symmetry protected topological phases in decorated dimer models

Author(s): Xu Yang, Shenghan Jiang, Ashvin Vishwanath, and Ying Ran Lieb-Schultz-Mattis (LSM) theorem and its various generalizations provide powerful guidance towards the search for novel phases of matter. Here, the authors propose and prove a generalized LSM theorem suitable for 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin in the unit cell. One outcome of this theorem is that, under certain conditions, the gapped ground states preserving all symmetries must be a nontrivial symmetry-protected topological (SPT) phase. Such symmetry-enforced SPTs display a dyonic character in that they associate charge with symmetry flux, which is demonstrated using quasiexactly solvable models constructed by decorating quantum dimer models.
[Phys. Rev. B 98, 125120] Published Mon Sep 10, 2018

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23:03 Editors' SuggestionsMany-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries

Author(s): Ken Shiozaki, Hassan Shapourian, Kiyonori Gomi, and Shinsei Ryu Here, the authors introduce a set of quantities to diagnose symmetry-protected topological phases of fermions protected by antiunitary symmetries. These quantities, which can be written as expectation values of nonlocal operators, effectively simulate the partition function on nonorientable spacetime manifolds in the operator formalism. The important observation is that the proposed quantities are complex valued for topological states, where the complex phase is the many-body topological invariant. Numerous symmetry classes and dimensionalities are studied in detail. The key ingredient of all quantities is the “fermionic partial transpose”. For example, the Z2 topological invariant for time-reversal symmetric topological insulators in two spatial dimensions is

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18:11 Editors' SuggestionsChiral topological phases from artificial neural networks

Author(s): Raphael Kaubruegger, Lorenzo Pastori, and Jan Carl Budich Artificial neural networks and machine learning tools have become ubiquitous far beyond the field of computer science. They already smartly assist us in our daily lives in various ways. Recently, these concepts have been adopted and applied in the realm of quantum physics, for example as a computational Ansatz for the state of a quantum many-body system. In this work, the authors harness the enormous flexibility of artificial neural networks to study exotic phases of quantum matter, known as chiral topological phases, that are particularly hard to investigate microscopically with more conventional computational methods.
[Phys. Rev. B 97, 195136] Published Fri May 18, 2018

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18:06 Editors' SuggestionsLearning disordered topological phases by statistical recovery of symmetry

Author(s): Nobuyuki Yoshioka, Yutaka Akagi, and Hosho Katsura Understanding the phases of a model usually requires knowledge of their characteristic features, which are nonlocal in topologically ordered systems. Here, the authors reframe the phase classification problem in disordered topological superconductors as a data-driven task, motivated by the recent surge of interest in the application of machine-learning techniques including deep learning. It is demonstrated that an artificial neural network learns to extract the essence of the clean system and successfully distinguishes phases even under disorder by statistical recovery of translational symmetry.
[Phys. Rev. B 97, 205110] Published Wed May 09, 2018

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23:16 Editors' SuggestionsTemperature-Induced Topological Phase Transition in HgTe Quantum Wells

Author(s): A. M. Kadykov, S. S. Krishtopenko, B. Jouault, W. Desrat, W. Knap, S. Ruffenach, C. Consejo, J. Torres, S. V. Morozov, N. N. Mikhailov, S. A. Dvoretskii, and F. Teppe The visualization of the Landau levels in HgTe/CdTe quantum wells at different temperatures allows the exploration of the phase diagram as a function of magnetic field and temperature.
[Phys. Rev. Lett. 120, 086401] Published Thu Feb 22, 2018

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23:14 Editors' SuggestionsFracton Topological Phases from Strongly Coupled Spin Chains

Author(s): Gábor B. Halász, Timothy H. Hsieh, and Leon Balents A realistic model of fracton topological phases using only two spins brings their experimental realization a step closer.
[Phys. Rev. Lett. 119, 257202] Published Wed Dec 20, 2017

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19:21 Editors' SuggestionsBuilding crystalline topological phases from lower-dimensional states

Author(s): Sheng-Jie Huang, Hao Song, Yi-Ping Huang, and Michael Hermele Topological phases protected by the geometrical symmetries of crystal lattices turn out to be surprisingly simple. They can be built from simpler lower-dimensional states, arranged in a crystalline pattern.
[Phys. Rev. B 96, 205106] Published Mon Nov 06, 2017

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16:50 ScienceDaily.comMissing link between new topological phases of matter discovered

Physicists have investigated a class of materials that exhibit characteristics of topological insulators. During these studies they discovered a transition between two different topological phases, one of which is ferroelectric.

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13:03 Phys.orgMissing link between new topological phases of matter discovered

Physicists at BESSY II have investigated a class of materials that exhibit characteristics of topological insulators. During these studies, they discovered a transition between two different topological phases, one of which is ferroelectric, meaning a phase in the material that exhibits spontaneous electric polarisation and can be reversed by an external electric field. This could also lead to new applications such as switching between differing conductivities.

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20:08 Editors' SuggestionsOne-dimensional symmetry protected topological phases and their transitions

Author(s): Ruben Verresen, Roderich Moessner, and Frank Pollmann The authors present a unified perspective on a large class of one-dimensional symmetry-protected topological phases. Characterizing critical points between such phases leads to a conjecture of a topological lower bound on the central charge in terms of the phase-specific edge mode dimension.
[Phys. Rev. B 96, 165124] Published Thu Oct 12, 2017

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00:07 Editors' SuggestionsExactly solvable models for symmetry-enriched topological phases

Author(s): Meng Cheng, Zheng-Cheng Gu, Shenghan Jiang, and Yang Qi Symmetry-enriched topological phases (SET) exhibit both long-range entanglement and intricate interplay with global symmetries, such as anyon permutation symmetry or fractionalization of quantum numbers, going beyond the Landau paradigm of symmetry breaking. Here, the authors study two-dimensional SET phases based on the novel concept of symmetric local unitary transformations. Using the fixed-point structure of wave functions, they construct systematically exactly solvable models that can describe generic nonchiral SET phases. The technique applies to on-site as well as spatial symmetries and, furthermore, to anomalous symmetries that can only be realized on the surface of three-dimensional symmetry-protected phases.
[Phys. Rev. B 96, 115107] Published Wed Sep 06, 2017

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19:28 Editors' SuggestionsCheshire charge in (3+1)-dimensional topological phases

Author(s): Dominic V. Else and Chetan Nayak The authors examine the phenomenon of “Cheshire charge” in topological phases of matter in three spatial dimensions. A looplike excitation is said to carry Cheshire charge if the charge is not locally detectable, that is, it can only be observed by a nonlocal process such as shrinking the loop to a point. The authors show that “Cheshire charge” is a generic feature of three-dimensional topological phases. They relate it to other features of these phases, such as three-loop braiding, as well as to higher-category theory that is hypothesized to be the general mathematical framework describing three-dimensional topological phases.
[Phys. Rev. B 96, 045136] Published Tue Jul 25, 2017

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18:38 Editors' SuggestionsFloquet topological phases protected by time glide symmetry

Author(s): Takahiro Morimoto, Hoi Chun Po, and Ashvin Vishwanath Nonequilibrium systems under periodic driving realize novel topological phases that cannot be achieved in equilibrium systems. One unique feature of periodically driven systems is that they can host a purely dynamical symmetry that involves time translation. This work explores a new class of Floquet topological phases protected by one realization of such dynamical symmetry, i.e., “time glide symmetry”, which is defined by a combination of reflection and time translation. Lattice models with time glide symmetric driving that are introduced show stable gapless surface states along with nontrivial topological numbers defined with time glide symmetry. In addition, a general classification theory of time glide symmetric topological phases is obtained by using a Clifford algebra

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21:36 Editors' SuggestionsMany-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries

Author(s): Ken Shiozaki, Hassan Shapourian, and Shinsei Ryu Finding suitable nonlocal order parameters that distinguish various symmetry-protected topological (SPT) phases is an important subject in view of experimental and numerical detection of SPT phases. By “simulating” the generating manifold of cobordism group in the operator formalism, the authors here propose nonlocal operations as diagnoses for SPT phases protected by point group symmetries. The nonlocal operations involve “partial point group transformations”, which are obtained by point group transformations restricted to a spatial subregion on a given ground-state wave function. Through analytical and numerical calculations, the authors show that the complex U(1) phase of the ground state expectation value of such partial point group transformations may serve as an order parameter

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19:09 Physics.Aps.orgViewpoint: Neural Networks Identify Topological Phases

Author(s): Juan Carrasquilla A new machine-learning algorithm based on a neural network can tell a topological phase of matter from a conventional one.
[Physics 10, 56] Published Mon May 22, 2017

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19:06 Editors' SuggestionsInteracting fermionic symmetry-protected topological phases in two dimensions

Author(s): Chenjie Wang, Chien-Hung Lin, and Zheng-Cheng Gu Symmetry-protected topological (SPT) phases (e.g., the well known topological insulators) are a class of energetically gapped condensed matter systems that exhibit interesting topological properties only in the presence of certain global symmetries. While a great understanding of noninteracting fermionic SPT phases has been achieved recently, interacting SPT phases, in particular those that exist only in strongly interacting systems, are much less understood in general. Here, the authors study strongly interacting fermionic SPT phases in two spatial dimensions with finite Abelian unitary symmetries and provide a potentially complete classification of them.
[Phys. Rev. B 95, 195147] Published Mon May 22, 2017

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18:01 Editors' SuggestionsFloquet topological phases with symmetry in all dimensions

Author(s): Rahul Roy and Fenner Harper Periodically driven Floquet systems can host dynamical phases, including a range of exotic topological phases that have no static analogs. This work presents a homotopy approach to the study of driven systems, which treats unitary evolutions as paths in the space of unitary operators. By considering loop evolutions in this space, the authors obtain a topological classification, free of uncertainties and ambiguities about the long-time robustness of of behavior in specific physical models. Two classes of Floquet symmetry-protected topological phase are identified, characterized by unitary evolutions that act trivially in the bulk but nontrivially at the boundary of an open system. The first class is captured by an explicit group cohomology construction; it has the remarkable property of converting a trivial

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21:15 Editors' SuggestionsAnyon condensation and a generic tensor-network construction for symmetry-protected topological phases

Author(s): Shenghan Jiang and Ying Ran Bosonic symmetry protected topological (SPT) phases are bosonic analogs of free-fermion topological insulators and superconductors, but require interactions to be realized. Previously, a wide range of bosonic SPT phases protected by on-site symmetries has been systematically investigated, which are found to be related to group cohomology theory. However, a systematic understanding of SPT phases protected by spatial symmetries is still lacking. Here, the authors present systematic constructions of tensor-network wave functions for bosonic SPT phases protected by a general symmetry group SG involving both on-site and spatial symmetries. They find, in spatial dimension d=1,2,3, that a wide range of bosonic SPT phases are classified by the group cohomology Hd+1SG,U(1), in which the time-reversal symmetry and

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17:19 Physics.Aps.orgFocus: Nobel Prize—Topological Phases of Matter

Author(s): Michael Schirber The 2016 Nobel Prize in Physics was awarded to theoretical physicists whose work established the role of topology in understanding exotic forms of matter.
[Physics 9, 116] Published Fri Oct 07, 2016

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13:13 Washington PostNobel jury praises physics winners for ‘discoveries of topological phase transitions and topological phases of matter’

Nobel jury praises physics winners for ‘discoveries of topological phase transitions and topological phases of matter’

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22:59 Editors' SuggestionsAnomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators

Author(s): Daniel Leykam, M. C. Rechtsman, and Y. D. Chong The design for a photonic lattice that can realize a previously unobserved anomalous Floquet phase is proposed.
[Phys. Rev. Lett. 117, 013902] Published Wed Jun 29, 2016

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16:24 Editors' SuggestionsPhase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

Author(s): C. W. von Keyserlingk and S. L. Sondhi Phases of matter are traditionally seen as families of static systems exhibiting the same long-distance and low-energy correlations. In this work, the authors propose and classify a new family of phases of matter. They are novel insofar as they are intrinsically driven and out of equilibrium — they can only be realized in systems with time-dependent Hamiltonians. The phases we consider arise in 1D periodically driven systems, in the presence of strong disorder and interactions, and are similar to but qualitatively distinct from the symmetry-protected topological phases now well known in the equilibrium setting. In a companion paper, the authors examine similar intrinsically driven families of states with long-range order, and an order parameter that oscillates at a frequency that is robustly an

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