scholarly journals Randomness of Eigenstates of Many-Body Quantum Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 227 ◽  
Author(s):  
Li-Zhen Sun ◽  
Qingmiao Nie ◽  
Haibin Li
Keyword(s):  
Hard Core ◽  
Underlying Mechanism ◽  
Quantum Systems ◽  
One Dimension ◽  
Many Body ◽  
Random Vectors ◽  
Boson System ◽  
Many Body Systems

The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies the integrable-chaos transition in this system.

scholarly journals Probing Many-Body Systems Near Spectral Degeneracies

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1796
Author(s):  
Klaus Ziegler
Keyword(s):  
Decay Rate ◽  
Correlation Matrix ◽  
Time Correlation ◽  
General Concept ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Many Body ◽  
Space Localization ◽  
Many Body Systems ◽  
Random Times

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.

Introduction to integrable many-body systems I

2008 ◽  
Vol 58 (6) ◽  
Author(s):  
Ladislav Šamaj
Keyword(s):  
Hard Core ◽  
Coulomb Gas ◽  
Quantum Gases ◽  
Many Body ◽  
One Dimensional ◽  
Introductory Course ◽  
Pairwise Interactions ◽  
Classical Models ◽  
Physical Level ◽  
Many Body Systems

Introduction to integrable many-body systems IThis is the first volume of a three-volume introductory course about integrable (exactly solvable) systems of interacting bodies. The aim of the course is to derive and analyze, on an elementary mathematical and physical level, the Bethe ansatz solutions, ground-state properties and the thermodynamics of integrable many-body systems in many domains of physics: Nonrelativistic one-dimensional continuum Fermi and Bose gases; One-dimensional quantum models of condensed matter physics like the Heisenberg, Hubbard and Kondo models; Relativistic models of the (1+1)-dimensional Quantum Field Theory like the Luttinger model, the sine-Gordon model and its fermionic analog the Thirring model; Two-dimensional classical models, especially the symmetric Coulomb gas. In the first part of this volume, we deal with nonrelativistic one-dimensional continuum Fermi and Bose quantum gases of spinless (identical) particles with specific types of pairwise interactions like the short-range δ-function and hard-core interactions, and the long-range 1/

scholarly journals Entanglement spreading and quasiparticle picture beyond the pair structure

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Alvise Bastianello ◽  
Mario Collura
Keyword(s):  
Quantum Systems ◽  
One Dimension ◽  
Many Body ◽  
Initial State ◽  
Perfect Agreement ◽  
Quasi Particle ◽  
Simple Assumption ◽  
The Common ◽  
Quasiparticle Picture ◽  
Number Of Particles

The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations' pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Rényi entropies. Our results are in perfect agreement with iTEBD numerical simulations.

PROJECTED ENTANGLED STATES: PROPERTIES AND APPLICATIONS

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5142-5153 ◽  
Author(s):  
F. VERSTRAETE ◽  
M. WOLF ◽  
D. PÉREZ-GARCÍA ◽  
J. I. CIRAC
Keyword(s):  
Numerical Algorithms ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
One Dimension ◽  
Entangled States ◽  
Matrix Product ◽  
Many Body ◽  
Many Body Systems ◽  
Dimension One

We present a new characterization of quantum states, what we call Projected Entangled-Pair States (PEPS). This characterization is based on constructing pairs of maximally entangled states in a Hilbert space of dimension D2, and then projecting those states in subspaces of dimension d. In one dimension, one recovers the familiar matrix product states, whereas in higher dimensions this procedure gives rise to other interesting states. We have used this new parametrization to construct numerical algorithms to simulate the ground state properties and dynamics of certain quantum-many body systems in two dimensions.

scholarly journals Scaling of the polarization amplitude in quantum many-body systems in one dimension

2018 ◽  
Vol 97 (16) ◽  
Author(s):  
Ryohei Kobayashi ◽  
Yuya O. Nakagawa ◽  
Yoshiki Fukusumi ◽  
Masaki Oshikawa
Keyword(s):  
One Dimension ◽  
Many Body ◽  
Many Body Systems

scholarly journals Experimental Test of Spontaneous Correlation and Anomalous Sensitivity in Finite Highly Excited Many-Body Systems

2003 ◽  
Vol 12 (03) ◽  
pp. 377-393 ◽  
Author(s):  
Qi Wang ◽  
Sergey Yu Kun ◽  
Wendong Tian ◽  
Songlin Li ◽  
Zhonghe Jiang ◽  
...  
Keyword(s):  
Cross Sections ◽  
Experimental Test ◽  
Heavy Ion ◽  
Quantum Systems ◽  
Slow Phase ◽  
Many Body ◽  
Ion Collisions ◽  
Excited Complex ◽  
Many Body Systems ◽  
Phase Randomization

We have tested recent suggestion of anomalous sensitivity in highly excited quantum many-body systems. Two independent measurements of cross sections for the 19 F + 93 Nb strongly dissipative heavy-ion collisions have been performed at incident energies from 102 to 108 MeV in steps of 250 keV. In the two measurements we used different, independently prepared, 93Nb target foils with nominally the same thickness. The data indicate statistically significant non-reproducibility of the energy oscillating yields in the two measurements. The observed non-reproducibility is consistent with recent theoretical arguments on spontaneous correlation, slow phase randomization and chaos in highly excited complex quantum systems.

scholarly journals Many-body localization: stability and instability

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160422 ◽  
Author(s):  
Wojciech De Roeck ◽  
John Z. Imbrie
Keyword(s):  
Higher Dimensions ◽  
Quantum Systems ◽  
One Dimension ◽  
Reasonable Assumption ◽  
Level Spacing ◽  
Weak Disorder ◽  
Many Body ◽  
Integrals Of Motion ◽  
Stability And Instability ◽  
Rare Regions

Rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. We describe a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension, under a physically reasonable assumption on the statistics of eigenvalues. We discuss ideas about the situation in higher dimensions, where one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. We argue that ergodicity is restored in dimension d >1, although equilibration should be extremely slow, similar to the dynamics of glasses. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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