Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

Abstract

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1)U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrixproductstate representation and the singlesite reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L=501L=501 while accounting for N_{\rm ph}=63 phonons per site with high precision in the CDW phase.

Charge density wave breakdown in a heterostructure with electron-phonon coupling

“…This regime is still clearly a candidate for other schemes to efficiently treat phonons, such as the one of Ref. [78]. In total, the limiting factor for our calculations in the metallic regime is the local bond dimension and obtaining a steady state.…”

“…Recently, in Ref. [78], Köhler et al suggested introducing bath sites, thus treating a doubled system but with a restored U(1) symmetry. The methodology was further applied to time-evolution calculations in Ref.…”

Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer

“…We overcome these issues by employing the newly developed method of projected-purification (PP) 33,52 . Within this approach we restore the U(1)-particle number conservation symmetry by doubling the size of the (phononic) system.…”

“…First, we compute the spectral density from ab-initio multireference quantum chemical calculations and determine the effect of the molecule's vibrational modes on the electronic overlap integrals to obtain an effective model, capturing the coupling between electronic states and vibrations. Employing the resulting microscopic model, we perform a simulation of the full post photo-excitation quantum dynamics using a novel method from tensor networks 33 . In particular, this method allows for the description of many bosonic degrees of freedom with a large number of internal states by dynamically selecting the relevant bosonic modes.…”

Spin-Holstein models in trapped-ion systems

“…(3) (see [15]). Note that more general approaches exist to tackle this issue and have been applied to problems with fermionphonon coupling [16][17][18][19][20][21].…”