arXiv subjects

Emanuel Casiano-Diaz

Publications and source records attributed to Emanuel Casiano-Diaz.

4 recordsLinked to original sources

arXiv2023

Reduction of Autocorrelation Times in Lattice Path Integral Quantum Monte Carlo via Direct Sampling of the Truncated Exponential Distribution

In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the probability distribution from which random variates are sampled, simulations can be made more efficient, by virtue of an autocorrelation time reduction. In this paper, we illustrate how to directly sample random variates from a two dimensional truncated exponential distribution. We show that our direct sampling approach converges faster to the target distribution compared to rejection sampling. The direct sampling of one and two dimensional truncated exponential distributions is then applied to a recent Path Integral Monte Carlo (PIMC) algorithm for the simulation of Bose-Hubbard lattice models at zero temperature. The new sampling method results in improved acceptance ratios and reduced autocorrelation times of estimators, providing an effective speed up of the simulation.

physics.comp-ph↗

arXiv2023

A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons

A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to $L=256$ sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.

cond-mat.quant-gas↗

arXiv2019

Operationally accessible entanglement of one dimensional spinless fermions

For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle number fluctuations.

quant-ph↗

arXiv2017

Particle partition entanglement of one dimensional spinless fermions

We investigate the scaling of the Rényi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second Rényi entanglement entropy and show that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional $t-V$ model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics supports its utility as a probe of quantum liquids.

cond-mat.quant-gas↗