Entanglement Continuous Unitary Transformations

Abstract

Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called "entanglement-CUT" or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We provide the general idea behind eCUT and explain its implementation for finite 1d systems using the formalism of matrix product operators. We also present proof-of-principle results for the spin-1/2 1d quantum Ising model and the 3-state quantum Potts model in a transverse field. Entanglement-CUTs can also be generalized to higher dimensions and to the thermodynamic limit.

7 pages, 3 figures, 1 algorithm. Revised version, to appear in EPL

References in corpus (15)

• Many body localization and thermalization in quantum statistical mechanics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Matrix product states represent ground states faithfully
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The iTEBD algorithm beyond unitary evolution
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Applying matrix product operators to model systems with long-range interactions
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
• Unifying variational methods for simulating quantum many-body systems
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• A generalized perspective on non-perturbative linked cluster expansions
• Truncation errors in self-similar continuous unitary transformations