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 The simulation of non-Abelian statistics of Majorana fermions in Ising chain with Z2 symmetry

2017 ◽  
Vol 31 (11) ◽  
pp. 1750123
Author(s):  
Xiao-Ming Zhao ◽  
Jing Yu ◽  
Jing He ◽  
Qiu-Bo Cheng ◽  
Ying Liang ◽  
...  
Keyword(s):  
Transverse Field ◽  
Spin Model ◽  
Majorana Fermions ◽  
Spin Representation ◽  
Ising Chain ◽  
Zero Energy ◽  
Topological Quantum ◽  
Transverse Field Ising Model ◽  
Topological Quantum Computation ◽  
Symmetry Protected

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation.

scholarly journals The bulk-corner correspondence of time-reversal symmetric insulators

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Sander Kooi ◽  
Guido van Miert ◽  
Carmine Ortix
Keyword(s):  
Time Reversal ◽  
Real Space ◽  
Topological Phases ◽  
Spin Orbit Coupling ◽  
Topological Properties ◽  
Many Body ◽  
Boundary Correspondence ◽  
Berry Phases ◽  
The Many ◽  
Do So

AbstractThe topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional topological properties that do not yield surface spectral features, but manifest themselves as (fractional) quantized electronic charges localized at the crystal boundaries. Here, we formulate such bulk-corner correspondence for the physical relevant case of materials with time-reversal symmetry and spin-orbit coupling. To do so we develop partial real-space invariants that can be neither expressed in terms of Berry phases nor using symmetry-based indicators. These previously unknown crystalline invariants govern the (fractional) quantized corner charges both of isolated material structures and of heterostructures without gapless interface modes. We also show that the partial real-space invariants are able to detect all time-reversal symmetric topological phases of the recently discovered fragile type.

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.

Few-electron quantum-dot spintronics

2017 ◽  
Author(s):  
D.V. Melnikov ◽  
J. Kim ◽  
L.-X. Zhang ◽  
J.-P. Leburton
Keyword(s):  
Electron System ◽  
Stability Diagram ◽  
Theoretical Description ◽  
Exact Diagonalization ◽  
Many Body ◽  
Approximate Methods ◽  
Diagonalization Method ◽  
The Stability ◽  
The Many ◽  
Exact Diagonalization Method

This article examines the spin and charge properties of double and triple quantum dots (QDs) populated containing just a few electrons, with particular emphasis on laterally coupled QDs. It first describes the theoretical approach, known as exact diagonalization method, utilized on the example of the two-electron system in coupled QDs that are modelled as two parabolas. The many-body problem is solved via the exact diagonalization method as well as variational Heitler–London and Monte Carlo methods. The article proceeds by considering the general characteristics of the two-electron double-QD structure and limitations of the approximate methods commonly used for its theoretical description. It also discusses the stability diagram for two circular dots and investigates how its features are affected by the QD elliptical deformations. Finally, it assesses the behavior of the two-electron system in the realistic double-dot confinement potentials.

Wave equation for dissipative systems derived from a quantized many-body problem

1980 ◽  
Vol 58 (7) ◽  
pp. 1019-1025 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Body Wave ◽  
Time Dependent ◽  
Dissipative Systems ◽  
Many Body ◽  
Dependent Part ◽  
The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

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