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We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Although trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial.
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Bond-dependent slave-particle cluster theory based on density matrix expansion
Efficient and accurate computational methods for dealing with interacting electron problems on a lattice are of broad interest to the condensed matter community. For interacting Hubbard models, we introduce a cluster slave-particle approach that provides significant computational savings with high accuracy for total energies, site occupancies, and interaction energies. Compared to exact benchmarks using density matrix renormalization group for d-p Hubbard models, our approach delivers accurate results using two to three orders of magnitude lower computational cost. Our method is based on a slave-particle decomposition with an improved description of particle hoppings, and a density matrix expansion method where the interacting lattice slave-particle problem is turned into a set of overlapping real-space clusters which are solved self-consistently with appropriate physical matching constraints at shared lattice sites between clusters.
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- Award ID(s):
- 2237469
- PAR ID:
- 10479699
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 107
- Issue:
- 11
- ISSN:
- 2469-9950
- Page Range / eLocation ID:
- 115153
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevB.107.115153
