Chia-Chen Chang

Recent advances in determinant quantum Monte Carlo

Abstract Determinant quantum Monte Carlo is a method for studying magnetic, transport and thermodynamic properties of interacting fermions on a lattice. It is widely used to explore the physics of strongly correlated quantum systems, from cuprate superconductors to ultracold atoms trapped on optical lattices. This paper contains a description of recent algorithmic advances in the determinant quantum Monte Carlo technique. Focus will be on algorithms developed for hybrid multicore processor and GPU platforms. The resulting speed-up of the simulations will be quantified. Simulations’ results will also be presented, with an emphasis on physical quantities that can now be computed for large numbers of sites.

Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices

Here, we calculate the bipartite R enyi entanglement entropy of an L x L x 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two L x L planes, and (ii) One that divides the lattice into two equal-size (L x L=2 x 2) bilayers. Furthermore, we compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as L2, while the latter scales with L with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We also comment on the large uncertainties in the numerical results with increasing U, which would have to be overcome before the critical behavior and logarithmic corrections can be quanti ed.

Advancing Large Scale Many-Body QMC Simulations on GPU Accelerated Multicore Systems

The Determinant Quantum Monte Carlo (DQMC) method is one of the most powerful approaches for understanding properties of an important class of materials with strongly interacting electrons, including magnets and superconductors. It treats these interactions exactly, but the solution of a system of N electrons must be extrapolated to bulk values. Currently N 500 is state-of-the-art. Increasing N is required before DQMC can be used to model newly synthesized materials like functional multilayers. DQMC requires millions of linear algebra computations of order N matrices and scales as N3. DQMC cannot exploit parallel distributed memory computers efficiently due to limited scalability with the small matrix sizes and stringent procedures for numerical stability. Today, the combination of multisocket multicore processors and GPUs provides widely available platforms with new opportunities for DQMC parallelization. The kernel of DQMC, the calculation of the Greens function, involves long products of matrices. For numerical stability, these products must be computed using graded decompositions generated by the QR decomposition with column pivoting. The high communication overhead of pivoting limits parallel efficiency. In this paper, we propose a novel approach that exploits the progressive graded structure to reduce the communication costs of pivoting. We show that this method preserves the same numerical stability and achieves 70% performance of highly optimized DGEMM on a two-socket six-core Intel processor. We have integrated this new method and other parallelization techniques into QUEST, a modern DQMC simulation package. Using 36 hours on this Intel processor, we are able to compute accurately the magnetic properties and Fermi surface of a system of N = 1024 electrons. This simulation is almost an order of magnitude more difficult than N 500, owing to the N3 scaling. This increase in system size will allow, for the first time, the computation of the magnetic and transport properties of layered materials with DQMC. In addition, we show preliminary results which further accelerate DQMC simulations by using GPU processors.

Localization of Interacting Dirac Fermions

We study the effect of disorder on the semimetal – Mott insulator transition in the half-filled repulsive Hubbard model on a honeycomb lattice, a system that features vanishing density of states at the Fermi level. Using the determinant quantum Monte Carlo method, we characterize various phases in terms of the bulk-limit antiferromagnetic (AF) order parameter, compressibility, and temperature-dependent DC conductivity. In the clean limit, our data are consistent with previous results showing a single quantum critical point separating the semi-metallic and AF Mott insulating phases. With the presence of randomness, a non-magnetic disordered insulating phase emerges. Inside this disordered insulator phase, there is a crossover from a gapless Anderson-like insulator to a gapped Mott-like insulator.

Competing exotic quantum phases of spin- 12 ultracold lattice bosons with extended spin interactions

Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as 87Rb, 39K or 23Na in the F = 1 hyperfine state offer an ideal platform for studying the interplay of super fluidity and quantum magnetism. Motivated by the experimental developments, we study ground state phases of a two-component Bose gas loaded on an optical lattice. We describe this effectively by the Bose-Hubbard Hamiltonian with onsite and near neighbor spin-spin interactions. One important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Furthermore, using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators, ferromagnetic and AF super fluids.

Discriminating antiferromagnetic signatures in systems of ultracold fermions by tunable geometric frustration

Recently, it has become possible to tune optical lattices continuously between square and triangular geometries. We compute thermodynamics and spin correlations in the corresponding Hubbard model using determinant quantum Monte Carlo and show that the frustration effects induced by the variable hopping terms can be clearly separated from concomitant bandwidth changes by a proper rescaling of the interaction. An enhancement of the double occupancy by geometric frustration signals the destruction of nontrivial antiferromagnetic correlations at weak coupling and entropy

Quantum disordered phase near the Mott transition in the staggered-flux Hubbard model on a square lattice.

s\lesssim \ln(2)

A correlated Anderson insulator on the honeycomb lattice

(and restores Pomeranchuk cooling at strong frustration), paving the way to the long-sought experimental detection of antiferromagnetism in ultracold fermions on optical lattices.