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 GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

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 Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning

Science ◽  
2019 ◽  
Vol 365 (6457) ◽  
pp. eaaw1147 ◽  
Author(s):  
Frank Noé ◽  
Simon Olsson ◽  
Jonas Köhler ◽  
Hao Wu
Keyword(s):  
Molecular Dynamics ◽  
Deep Learning ◽  
Statistical Mechanics ◽  
Equilibrium Distribution ◽  
Condensed Matter ◽  
Computational Effort ◽  
Equilibrium States ◽  
Many Body ◽  
Reaction Coordinates ◽  
Many Body Systems

Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in “one shot,” vast computational effort is invested for simulating these systems in small steps, e.g., using molecular dynamics. Combining deep learning and statistical mechanics, we developed Boltzmann generators, which are shown to generate unbiased one-shot equilibrium samples of representative condensed-matter systems and proteins. Boltzmann generators use neural networks to learn a coordinate transformation of the complex configurational equilibrium distribution to a distribution that can be easily sampled. Accurate computation of free-energy differences and discovery of new configurations are demonstrated, providing a statistical mechanics tool that can avoid rare events during sampling without prior knowledge of reaction coordinates.

Geometric Phase in Condensed Matter III: Many-Body Systems

2003 ◽  
pp. 337-359
Author(s):  
Arno Bohm ◽  
Ali Mostafazadeh ◽  
Hiroyasu Koizumi ◽  
Qian Niu ◽  
Joseph Zwanziger
Keyword(s):  
Geometric Phase ◽  
Condensed Matter ◽  
Many Body ◽  
Many Body Systems

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 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 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.

scholarly journals EXACT RESULTS FOR THE ONE-DIMENSIONAL MANY-BODY PROBLEM WITH CONTACT INTERACTION: INCLUDING A TUNABLE IMPURITY

2007 ◽  
Vol 19 (04) ◽  
pp. 349-370 ◽  
Author(s):  
V. CAUDRELIER ◽  
N. CRAMPÉ
Keyword(s):  
Bethe Ansatz ◽  
Contact Interaction ◽  
Bound States ◽  
Condensed Matter ◽  
Many Body ◽  
One Dimensional ◽  
Special Cases ◽  
Exactly Solvable ◽  
Bethe Equations ◽  
The One

The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine a stationary state asymmetrically. This could have interesting applications in condensed matter physics.

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