scholarly journals Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries

2017 ◽  
Vol 95 (20) ◽  
Author(s):  
Ken Shiozaki ◽  
Hassan Shapourian ◽  
Shinsei Ryu
Keyword(s):  
Point Group ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Symmetry Protected ◽  
Group Symmetries

scholarly journals Many-body topological invariants from randomized measurements in synthetic quantum matter

2020 ◽  
Vol 6 (15) ◽  
pp. eaaz3666 ◽  
Author(s):  
Andreas Elben ◽  
Jinlong Yu ◽  
Guanyu Zhu ◽  
Mohammad Hafezi ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Body Wave ◽  
Complete Classification ◽  
Theoretical Description ◽  
Spin Model ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Topological Quantum ◽  
The Many ◽  
Symmetry Protected

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

scholarly journals Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 541 ◽  
Author(s):  
Venkata Kota ◽  
Narendra Chavda
Keyword(s):  
Hermite Polynomials ◽  
Point Group ◽  
Majorana Fermions ◽  
Many Body ◽  
Boson Systems ◽  
Random Matrix Ensembles ◽  
Isolated Systems ◽  
Group Symmetries ◽  
Statistical Relaxation

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

scholarly journals Floquet Second-Order Topological Phases in Momentum Space

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1170
Author(s):  
Longwen Zhou
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Second Order ◽  
Large Integer ◽  
Open Boundary ◽  
Topological Invariants ◽  
Topological Phases ◽  
Open Boundary Conditions ◽  
Kicked Rotor ◽  
Symmetry Protected

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

Theoretical construction of weak topological crystalline insulators

2017 ◽  
Vol 31 (20) ◽  
pp. 1750136
Author(s):  
Qing-Li Zhu ◽  
Liang Hua ◽  
Ji-Mei Shen
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Discrete Symmetry ◽  
Topological Phases ◽  
Symmetry Classes ◽  
New Type ◽  
Theoretical Construction ◽  
Topological Crystalline Insulators ◽  
Group Symmetries

Inspired by the discovery of topological crystalline insulators (TCIs) in three-dimensional materials such as Pb[Formula: see text]Sn[Formula: see text]Se(Te), the classification of topological insulators has been extended to other discrete symmetry classes such as crystal point group symmetries. In this paper, we construct and study a simple model of weak TCIs, which will serve as a more viable project in the experimental probe for such new type of topological phases.

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