Exact solvability of interacting many body lattice systems

2010 ◽  
Vol 41 (4) ◽  
pp. 471-507 ◽  
Author(s):  
Boyka Aneva
Keyword(s):  
Many Body ◽  
Lattice Systems ◽  
Exact Solvability

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 Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 556
Author(s):  
Giovanni Cataldi ◽  
Ashkan Abedi ◽  
Giuseppe Magnifico ◽  
Simone Notarnicola ◽  
Nicola Dalla Pozza ◽  
...  
Keyword(s):  
Transverse Field ◽  
Matrix Product ◽  
Hilbert Curve ◽  
Many Body ◽  
Network Efficiency ◽  
Lattice Systems ◽  
Tensor Network ◽  
Quantum Ising Model ◽  
1D Chain ◽  
Numerical Precision

We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to 64×64, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.

scholarly journals On the absence of stationary currents

2020 ◽  
pp. 2060011
Author(s):  
Sven Bachmann ◽  
Martin Fraas
Keyword(s):  
Cross Section ◽  
Higher Dimensions ◽  
Quantum Systems ◽  
Total Current ◽  
Many Body ◽  
Lattice Systems ◽  
Volume Limit ◽  
Quantum Lattice Systems ◽  
The Many ◽  
Large Volume Limit

We review the proofs of a theorem of Bloch on the absence of macroscopic stationary currents in quantum systems. The standard proof shows that the current in 1D vanishes in the large volume limit under rather general conditions. In higher dimensions, the total current across a cross-section does not need to vanish in gapless systems but it does vanish in gapped systems. We focus on the latter claim and give a self-contained proof motivated by a recently introduced index for the many-body charge transport in quantum lattice systems having a conserved [Formula: see text]-charge.

ELECTRON SPIN RESONANCE AS A PROBE OF COLLECTIVE MODES IN ANISOTROPIC EXCHANGE-COUPLED PARAMAGNETS

2012 ◽  
Vol 26 (29) ◽  
pp. 1230021 ◽  
Author(s):  
D. L. HUBER
Keyword(s):  
Electron Spin Resonance ◽  
Electron Spin ◽  
Kondo Lattice ◽  
Collective Modes ◽  
Many Body ◽  
Lattice Systems ◽  
Strongly Coupled ◽  
Spin Resonance ◽  
Anisotropic Exchange ◽  
G Factors

Electron spin resonance (ESR) in exchanged-coupled paramagnets is a probe of field-dependent collective modes in a strongly coupled many-body system. We utilize a previously developed approach for the analysis of collective modes in such systems to express the experimentally determined g-factors of the ESR modes in an anisotropic magnet in terms of the microscopic (isolated spin) g-factors and the ratios of the static susceptibilities along the principal directions. Applications of the theory to the ferromagnetic insulator CrBr 3 and the Kondo lattice systems YbRh 2 Si 2, YbCo 2 Si 2, YbIr 2 Si 2 and CeRuPO are discussed.

scholarly journals Selected applications of typicality to real-time dynamics of quantum many-body systems

2020 ◽  
Vol 75 (5) ◽  
pp. 421-432 ◽  
Author(s):  
Tjark Heitmann ◽  
Jonas Richter ◽  
Dennis Schubert ◽  
Robin Steinigeweg
Keyword(s):  
Gibbs State ◽  
Transport Coefficients ◽  
Linear Response Theory ◽  
Numerical Approach ◽  
Many Body ◽  
Lattice Systems ◽  
Initial State ◽  
Time Dynamics ◽  
Many Body Systems ◽  
Low Dimensional

AbstractLoosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e. g., linear response theory (LRT). Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

scholarly journals Droplet tilings for rapid exploration of spatially constrained many-body systems

2021 ◽  
Vol 118 (34) ◽  
pp. e2020014118
Author(s):  
Anton Molina ◽  
Shailabh Kumar ◽  
Stefan Karpitschka ◽  
Manu Prakash
Keyword(s):  
Degrees Of Freedom ◽  
Experimental System ◽  
High Energy ◽  
Geometric Constraints ◽  
Material Behavior ◽  
Two Dimensional ◽  
Many Body ◽  
Lattice Systems ◽  
Initial State ◽  
Many Body Systems

Geometry in materials is a key concept which can determine material behavior in ordering, frustration, and fragmentation. More specifically, the behavior of interacting degrees of freedom subject to arbitrary geometric constraints has the potential to be used for engineering materials with exotic phase behavior. While advances in lithography have allowed for an experimental exploration of geometry on ordering that has no precedent in nature, many of these methods are low throughput or the underlying dynamics remain difficult to observe directly. Here, we introduce an experimental system that enables the study of interacting many-body dynamics by exploiting the physics of multidroplet evaporation subject to two-dimensional spatial constraints. We find that a high-energy initial state of this system settles into frustrated, metastable states with relaxation on two timescales. We understand this process using a minimal dynamical model that simulates the overdamped dynamics of motile droplets by identifying the force exerted on a given droplet as being proportional to the two-dimensional vapor gradients established by its neighbors. Finally, we demonstrate the flexibility of this platform by presenting experimental realizations of droplet−lattice systems representing different spin degrees of freedom and lattice geometries. Our platform enables a rapid and low-cost means to directly visualize dynamics associated with complex many-body systems interacting via long-range interactions. More generally, this platform opens up the rich design space between geometry and interactions for rapid exploration with minimal resources.

scholarly journals GROUND STATE OF MANY-BODY LATTICE SYSTEMS VIA A CENTRAL LIMIT THEOREM

2006 ◽  
Vol 20 (19) ◽  
pp. 2770-2778 ◽  
Author(s):  
CARLO PRESILLA ◽  
MASSIMO OSTILLI
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Ground State ◽  
Probabilistic Representation ◽  
Many Body ◽  
Lattice Systems ◽  
Time Approximation ◽  
Novel Approach ◽  
Long Time

We review a novel approach to evaluate the ground-state properties of many-body lattice systems based on an exact probabilistic representation of the dynamics and its long time approximation via a central limit theorem. The choice of the asymptotic density probability used in the calculation is discussed in detail.

scholarly journals Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Thomas Köhler ◽  
Jan Stolpp ◽  
Sebastian Paeckel
Keyword(s):  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Many Body ◽  
Lattice Systems ◽  
Quantum Lattice ◽  
Efficient Treatment ◽  
Half Filling ◽  
Low Dimensional ◽  
Reduced Density

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1)U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrixproductstate representation and the singlesite reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L=501L=501 while accounting for N_{\rm ph}=63 phonons per site with high precision in the CDW phase.

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