scholarly journals Void formation in operator growth, entanglement, and unitarity

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hong Liu ◽  
Shreya Vardhan
Keyword(s):  
Chaotic Systems ◽  
Probability Distributions ◽  
Void Formation ◽  
Multipartite Entanglement ◽  
Many Body ◽  
Maximal Entanglement ◽  
Void Distribution ◽  
Universal Feature ◽  
Many Body Systems ◽  
The One

Abstract The structure of the Heisenberg evolution of operators plays a key role in explaining diverse processes in quantum many-body systems. In this paper, we discuss a new universal feature of operator evolution: an operator can develop a void during its evolution, where its nontrivial parts become separated by a region of identity operators. Such processes are present in both integrable and chaotic systems, and are required by unitarity. We show that void formation has important implications for unitarity of entanglement growth and generation of mutual information and multipartite entanglement. We study explicitly the probability distributions of void formation in a number of unitary circuit models, and conjecture that in a quantum chaotic system the distribution is given by the one we find in random unitary circuits, which we refer to as the random void distribution. We also show that random unitary circuits lead to the same pattern of entanglement growth for multiple intervals as in (1 + 1)-dimensional holographic CFTs after a global quench, which can be used to argue that the random void distribution leads to maximal entanglement growth.

scholarly journals Non-equilibrium dynamics of an ultracold Bose gas under multi-pulsed interaction quenches

2016 ◽  
Vol 30 (30) ◽  
pp. 1650367 ◽  
Author(s):  
Lei Chen ◽  
Zhidong Zhang ◽  
Zhaoxin Liang
Keyword(s):  
Bose Gas ◽  
Quantum Gases ◽  
Zero Temperature ◽  
Many Body ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Multiple Interaction ◽  
The One ◽  
Body Correlation ◽  
Non Equilibrium

We investigate the non-equilibrium properties of a weakly interacting Bose gas subjected to a multi-pulsed quench at zero temperature, where the interaction parameter in the Hamiltonian system switches between values [Formula: see text] and [Formula: see text] for multiple times. The one-body and two-body correlation functions as well as Tan’s contact are calculated. The quench induced excitations are shown to increase with the number of quenches for both [Formula: see text] and [Formula: see text]. This implies the possibility to use multi-pulsed quantum quench as a more powerful way as compared to the “one-off” quench in controllable explorations of non-equilibrium quantum many-body systems. In addition, we study the ultra-short-range property of the two-body correlation function after multiple interaction quenches, which can serve as a probe of the “Tan’s contact” in the experiments. Our findings allow for an experimental probe using state of the art techniques with ultracold quantum gases.

scholarly journals ENTANGLEMENT PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4041-4057
Author(s):  
J. W. CLARK ◽  
A. MANDILARA ◽  
M. L. RISTIG ◽  
K. E. KÜRTEN
Keyword(s):  
Quantum Phase Transitions ◽  
Body Wave ◽  
Wave Functions ◽  
Von Neumann Entropy ◽  
Many Body ◽  
Lattice Systems ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Many Body Systems ◽  
The One

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

scholarly journals Statistics of correlation functions in the random Heisenberg chain

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Luis A. Colmenarez ◽  
Paul A. McClarty ◽  
Masud Haque ◽  
David J. Luitz
Keyword(s):  
Correlation Functions ◽  
Heavy Tails ◽  
Probability Distributions ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Spin Flip ◽  
Local Operators ◽  
Many Body Systems ◽  
Degenerate Perturbation Theory

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) – at least in one dimensional systems – leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder – in the thermal phase – we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in S_i^z S_{i+r}^zSizSi+rz correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the S_i^zS_{i+r}^zSizSi+rz correlator exhibits striking differences between the MBL and Anderson insulator cases.

Quantum Ensembles

2019 ◽  
pp. 285-296
Author(s):  
Robert H. Swendsen
Keyword(s):  
Statistical Mechanics ◽  
Probability Distributions ◽  
Quantum Statistical Mechanics ◽  
Stationary States ◽  
Mechanical State ◽  
Many Body ◽  
Model Probability ◽  
Exact Position ◽  
Quantum Statistical ◽  
Many Body Systems

The study of quantum statistical mechanics begins with a review of the basic principles of quantum mechanics. Schrödinger’s equation is introduced and Eigenstates (or stationary states) are defined. Model probability for quantum statistics is assumed to have a uniform distribution in phases. Wave functions for many-body systems are defined. The density matrix is introduced. The Planck entropy and the microcanonical ensemble are defined. The differences between classical and quantum statistical mechanics are all based on the differing concepts of a microscopic ‘state’. While the classical microscopic state (specified by a point in phase space) determines the exact position and momentum of every particle, the quantum mechanical state determines neither; quantum states can only provide probability distributions for observable quantities.

scholarly journals Maxwell electromagnetism as an emergent phenomenon in condensed matter

2016 ◽  
Vol 374 (2075) ◽  
pp. 20160093 ◽  
Author(s):  
J. Rehn ◽  
R. Moessner
Keyword(s):  
Magnetic Monopole ◽  
Condensed Matter ◽  
Many Body ◽  
Classical Electromagnetism ◽  
Magnetic Dipoles ◽  
Translational Invariance ◽  
Energy Behaviour ◽  
Many Body Systems ◽  
The One ◽  
Simple Systems

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognized much later. Here, we provide an account of how simple systems of localized spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalization of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism. This article is part of the themed issue ‘Unifying physics and technology in light of Maxwell's equations’.

scholarly journals Bell correlations at finite temperature

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 107 ◽  
Author(s):  
Matteo Fadel ◽  
Jordi Tura
Keyword(s):  
Bell Inequality ◽  
Bell Inequalities ◽  
Spin Systems ◽  
Squeezed States ◽  
Many Body ◽  
Quantum Harmonic Oscillator ◽  
Many Body Systems ◽  
Infinite Range Interactions ◽  
The One ◽  
Infinite Range

We show that spin systems with infinite-range interactions can violate at thermal equilibrium a multipartite Bell inequality, up to a finite critical temperature Tc. Our framework can be applied to a wide class of spin systems and Bell inequalities, to study whether nonlocality occurs naturally in quantum many-body systems close to the ground state. Moreover, we also show that the low-energy spectrum of the Bell operator associated to such systems can be well approximated by the one of a quantum harmonic oscillator, and that spin-squeezed states are optimal in displaying Bell correlations for such Bell inequalities.

DENSITY-MATRIX RENORMALISATION GROUP FOR DYNAMIC CORRELATION FUNCTIONS

2003 ◽  
Vol 17 (28) ◽  
pp. 5453-5457
Author(s):  
E. JECKELMANN
Keyword(s):  
Density Matrix ◽  
Variational Problem ◽  
Correlation Functions ◽  
Renormalisation Group ◽  
Many Body ◽  
Dynamic Correlation ◽  
Many Body Systems ◽  
The One ◽  
Low Dimensional ◽  
Insulating Phase

The calculation of dynamic correlation functions in quantum systems is formulated as a variational problem. For low-dimensional many-body systems this variational problem can be solved numerically using the density-matrix renormalisation group (DMRG). This dynamic DMRG method is demonstrated on the linear optical conductivity in the Mott insulating phase of the one-dimensional extended Hubbard model at half filling. The full optical spectrum of this model can be calculated almost exactly for chains with more than 100 sites, which is large enough to investigate the spectral properties in the thermodynamic limit. The accuracy of the method is illustrated by comparison with analytical results in the field-theoretical regime and in the strong-coupling limit.

scholarly journals Random matrix theory of the isospectral twirling

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Salvatore Francesco Emanuele Oliviero ◽  
Lorenzo Leone ◽  
Francesco Caravelli ◽  
Alioscia Hamma
Keyword(s):  
Mutual Information ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Dynamics ◽  
Matrix Theory ◽  
Probability Distributions ◽  
Equilibrium States ◽  
Many Body ◽  
Many Body Systems ◽  
Integrable Dynamics

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref. [1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

scholarly journals Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

2018 ◽  
Author(s):  
Johannes Hauschild ◽  
Frank Pollmann
Keyword(s):  
Matrix Product ◽  
Many Body ◽  
Density Matrix Renormalization ◽  
Tensor Networks ◽  
Condensed Matter Theory ◽  
Tensor Network ◽  
Matter Theory ◽  
Particle Number Conservation ◽  
Many Body Systems ◽  
The One

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

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