Symmetry Conserving Purification of Quantum States within the Density Matrix Renormalization Group

TL;DR

This paper enhances the ancilla method within the density matrix renormalization group framework to efficiently compute finite-temperature properties of quantum many-body systems, extending its applicability beyond spin models.

Contribution

It introduces improvements to the ancilla method by working on reduced Hilbert spaces and employing canonical approaches, broadening its use to t-J and Hubbard models.

Findings

Improved performance of the ancilla method for finite-temperature calculations.

Extended applicability of the method to t-J and Hubbard models.

Enhanced efficiency in computing thermodynamic quantities.

Abstract

The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero temperature or ground-state properties of one dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. We furthermore explore its applicability beyond spins systems to t-J and Hubbard models.