Generalization of Tomonaga–Luttinger Liquids and the Calogero–Sutherland Model: Microscopic Models for the Haldane Liquids

1998 ◽  
Vol 12 (16) ◽  
pp. 607-614 ◽  
Author(s):  
Kazumoto Iguchi
Keyword(s):  
Fermi Surface ◽  
Higher Dimensions ◽  
One Dimension ◽  
Body System ◽  
Many Body ◽  
Luttinger Liquids ◽  
Microscopic Models ◽  
Sutherland Model ◽  
Body Potential

We discuss the quantum many-body system interacting with a separately symmetric two-body potential in higher dimensions as a generalization of the Calogero–Sutherland model in one dimension. This system exhibits the properties of a Haldane liquid such as Haldane–Wu (i.e., fractional exclusion) statistics, broken particle–hole symmetry and the existence of pseudo-Fermi surface as a generalization of the cencept of Tomonaga–Luttinger liquids in one dimension.

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 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’.

scholarly journals Parent Hamiltonians of Jastrow wavefunctions

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Mathieu Beau ◽  
Adolfo del Campo
Keyword(s):  
Yukawa Potential ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Spatial Dimension ◽  
Many Body ◽  
Bright Soliton Solution ◽  
Pairwise Product ◽  
Three Body ◽  
Body Potential ◽  
Pair Function

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to an arbitrary spatial dimension. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.

Data-Driven Many-Body Models with Chemical Accuracy for CH4/H2O Mixtures

2020 ◽  
Author(s):  
Marc Riera ◽  
Alan Hirales ◽  
Raja Ghosh ◽  
Francesco Paesani
Keyword(s):  
Liquid Phase ◽  
Quantitative Description ◽  
Liquid Mixtures ◽  
Many Body ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Dynamics Simulations ◽  
Body Potential ◽  
Small Clusters ◽  
Many Body Interactions

<div> <div> <div> <p>Many-body potential energy functions (PEFs) based on the TTM-nrg and MB-nrg theoretical/computational frameworks are developed from coupled cluster reference data for neat methane and mixed methane/water systems. It is shown that that the MB-nrg PEFs achieve subchemical accuracy in the representation of individual many-body effects in small clusters and enables predictive simulations from the gas to the liquid phase. Analysis of structural properties calculated from molecular dynamics simulations of liquid methane and methane/water mixtures using both TTM-nrg and MB-nrg PEFs indicates that, while accounting for polarization effects is important for a correct description of many-body interactions in the liquid phase, an accurate representation of short-range interactions, as provided by the MB-nrg PEFs, is necessary for a quantitative description of the local solvation structure in liquid mixtures. </p> </div> </div> </div>

scholarly journals The phase diagram of carbon dioxide from correlation functions and a many-body potential

2021 ◽  
Vol 155 (2) ◽  
pp. 024503
Author(s):  
Amanda A. Chen ◽  
Alexandria Do ◽  
Tod A. Pascal
Keyword(s):  
Carbon Dioxide ◽  
Phase Diagram ◽  
Correlation Functions ◽  
Many Body ◽  
Body Potential

scholarly journals Ultrafast dynamical Lifshitz transition

2021 ◽  
Vol 7 (17) ◽  
pp. eabd9275
Author(s):  
Samuel Beaulieu ◽  
Shuo Dong ◽  
Nicolas Tancogne-Dejean ◽  
Maciej Dendzik ◽  
Tommaso Pincelli ◽  
...  
Keyword(s):  
Fermi Surface ◽  
Colossal Magnetoresistance ◽  
Surface Topology ◽  
Strongly Correlated ◽  
Many Body ◽  
Time Resolved ◽  
Weyl Semimetal ◽  
Lifshitz Transition ◽  
Fermi Surface Topology ◽  
Many Body Systems

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal Td-MoTe2. We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.

scholarly journals $$\hbox {Ag}_{m} \hbox {Rh}_n$$ clusters with $$m+n\le 55$$

2021 ◽  
Vol 140 (4) ◽  
Author(s):  
Nicolas Louis ◽  
Stephan Kohaut ◽  
Michael Springborg
Keyword(s):  
Genetic Algorithms ◽  
Structure Optimization ◽  
Structural Similarity ◽  
Similarity Function ◽  
Many Body ◽  
Coordination Numbers ◽  
Energetic Properties ◽  
Ag Clusters ◽  
Body Potential ◽  
Mixed Clusters

AbstractUsing a combination of genetic algorithms for the unbiased structure optimization and a Gupta many-body potential for the calculation of the energetic properties of a given structure, we determine the putative total-energy minima for all $$\hbox {Ag}_{m} \hbox {Rh}_n$$ Ag m Rh n clusters with a total number of atoms $$m+n$$ m + n up to 55. Subsequently, we use various descriptors to analyze the obtained structural and energetic properties. With the help of a similarity function, we show that the pure Ag and Rh clusters are structurally similar for sizes up to around 20 atoms. The same approach gives that the mixed clusters tend to possess a larger structural similarity with the pure Rh clusters than with the pure Ag clusters. However, for clusters with $$m\simeq n\ge 25$$ m ≃ n ≥ 25 , other structures dominate. The effective coordination numbers for the Ag and Rh atoms as well as the radial distributions of those atoms indicate that there is a tendency towards segregation with Rh atoms forming an inner part and the Ag atoms forming a shell. Only few clusters, all with a fairly large total number of atoms, are found to be particularly stable.

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