arXiv subjects

Rongzheng He

Publications and source records attributed to Rongzheng He.

4 recordsLinked to original sources

arXiv2021

Quantum Many-Body Calculations using Body-Centered Cubic Lattices

It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this work we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down fermions in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy $E_{\rm FG}$, we find that the ground state energy is $E_0/E_{\rm FG}= 0.369(2), 0.371(2),$ using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice \cite{He:2019ipt}. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size lattice artifacts in simulations of continuum quantum many-body systems.

cond-mat.quant-gas↗

arXiv2020

Superfluid Condensate Fraction and Pairing Wave Function of the Unitary Fermi Gas

The unitary Fermi gas is a many-body system of two-component fermions with zero-range interactions tuned to infinite scattering length. Despite much activity and interest in unitary Fermi gases and its universal properties, there have been great difficulties in performing accurate calculations of the superfluid condensate fraction and pairing wave function. In this work we present auxiliary-field lattice Monte Carlo simulations using a novel lattice interaction which accelerates the approach to the continuum limit, thereby allowing for robust calculations of these difficult observables. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down particles. As a fraction of the free Fermi gas energy $E_{FG}$, we find $E_0/E_{FG}= 0.369(2), 0.372(2)$, using two different definitions of the finite-system energy ratio, in agreement with the latest theoretical and experimental results. We then determine the condensate fraction by measuring off-diagonal long-range order in the two-body density matrix. We find that the fraction of condensed pairs is $α= 0.43(2)$. We also extract the pairing wave function and find the pair correlation length to be $ζ_pk_F = 1.8(3) \hbar$, where $k_F$ is the Fermi momentum. Provided that the simulations can be performed without severe sign oscillations, the methods we present here can be applied to superfluid neutron matter as well as more exotic P-wave and D-wave superfluids.

cond-mat.quant-gas↗

arXiv2019

Time fractals and discrete scale invariance with trapped ions

We show that a one-dimensional chain of trapped ions can be engineered to produce a quantum mechanical system with discrete scale invariance and fractal-like time dependence. By discrete scale invariance we mean a system that replicates itself under a rescaling of distance for some scale factor, and a time fractal is a signal that is invariant under the rescaling of time. These features are reminiscent of the Efimov effect, which has been predicted and observed in bound states of three-body systems. We demonstrate that discrete scale invariance in the trapped ion system can be controlled with two independently tunable parameters. We also discuss the extension to n-body states where the discrete scaling symmetry has an exotic heterogeneous structure. The results we present can be realized using currently available technologies developed for trapped ion quantum systems.

cond-mat.quant-gas↗

arXiv2018

Eigenvector continuation with subspace learning

A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this work we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.

nucl-th↗