scholarly journals Lieb–Robinson bounds and growth of correlations in Bose mixtures

2021 ◽  
pp. 1-27
Author(s):  
Alessandro Michelangeli ◽  
Nicola Santamaria
Keyword(s):  
Time Evolution ◽  
Correlation Functions ◽  
Ad Hoc ◽  
Controlled Growth ◽  
Bose Gases ◽  
Disjoint Sets ◽  
Number Of Particles

For a mixture of interacting Bose gases initially prepared in a regime of condensation (uncorrelation), it is proved that in the course of the time evolution observables of disjoint sets of particles of each species have correlation functions that remain asymptotically small in the total number of particles and display a controlled growth in time. This is obtained by means of ad hoc estimates of Lieb–Robinson type on the propagation of the interaction, established here for the multi-component Bose mixture.

Simulation of electrostatic systems in periodic boundary conditions. II. Equivalence of boundary conditions

1980 ◽  
Vol 373 (1752) ◽  
pp. 57-66 ◽  
Keyword(s):  
Dielectric Constant ◽  
Boundary Conditions ◽  
Correlation Functions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Perturbation Series ◽  
Large Sphere ◽  
Dipolar Systems ◽  
Simulation Cell ◽  
Number Of Particles

We consider simulations of dipolar systems under periodic boundary conditions in which a large sphere consisting of periodic replications of a central simulation cell is surrounded by a continuum of dielectric constant ε'. We develop a perturbation theory expressing correlation functions with ε" in terms of correlation functions with ε' exactly to order N* 1 , N being the number of particles in the sample. In the thermodynamic limit, the correlation functions and internal energy density are independent of e The Kirkwood g -factor is strongly dependent on ε ' but in such a way as to make the dielectric constant independent of ε'. The dependence upon ε' of h A {r) at large r, described in paper I, is explained in terms of the perturbation series.

scholarly journals Time Evolution of Correlation Functions in Quantum Many-Body Systems

2020 ◽  
Vol 124 (11) ◽  
Author(s):  
Álvaro M. Alhambra ◽  
Jonathon Riddell ◽  
Luis Pedro García-Pintos
Keyword(s):  
Time Evolution ◽  
Correlation Functions ◽  
Many Body ◽  
Many Body Systems

scholarly journals Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Claudius Hubig ◽  
Annabelle Bohrdt ◽  
Michael Knap ◽  
Fabian Grusdt ◽  
Ignacio Cirac
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Correlation Functions ◽  
Spin Correlation ◽  
Quantum States ◽  
Time Dependent ◽  
Two Dimensional ◽  
Quantum Gas ◽  
Expectation Values ◽  
Equal Time

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-Jt−J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

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