Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models

Abstract

In this work, a simple and fundamental numeric scheme dubbed as ab-initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly-correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: 1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimic the interactions between a supercell and the infinite environment, and the other give the ground state in a tensor network (TN) form. 2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite clue by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; 3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, and etc., providing a unified perspective that is previously missing in this fields; 4) AOP as well as TRD gives novel implications to existing TN-based algorithms: a modified iTEBD is suggested and the 2D AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state.

13 pages, 11 figures

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Cited by in corpus (12)

• A universal tensor network algorithm for any infinite lattice
• Few-body systems capture many-body physics: tensor network approach
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Efficient Quantum Simulation for Thermodynamics of Infinite-size Many-body Systems in Arbitrary Dimensions
• Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach
• Characterizing the quantum field theory vacuum using temporal Matrix Product states
• Controlling phase diagram of finite spin-$1/2$ chains by tuning boundary interactions
• Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
• Boundary-induced singularity in strongly-correlated quantum systems at finite temperature
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States
• Accurate simulation and thermal tuning by temperature-adaptive boundary interactions on quantum many-body systems