Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states - INSPIRE

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Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states

Oct 15, 2017

6 pages

Published in:

Phys.Rev.Lett. 121 (2018) 23, 230402

Published: Dec 8, 2018

e-Print:

1710.05397 [cond-mat.str-el]

DOI:

10.1103/PhysRevLett.121.230402

View in:

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Abstract: (APS)

We establish that a Bloch-state ansatz based on periodic uniform matrix product states (PUMPS), originally designed to capture single-quasiparticle excitations in gapped systems, is in fact capable of accurately approximating all low-energy eigenstates of critical quantum spin chains on the circle. When combined with the methods of [Milsted and Vidal, Phys. Rev. B 96, 245105PRBMDO2469-995010.1103/PhysRevB.96.245105] based on the Koo-Saleur formula, PUMPS Bloch states can then be used to identify each low-energy eigenstate of a chain made of up to hundreds of spins with its corresponding scaling operator in the emergent conformal field theory (CFT). This enables the following two tasks that we demonstrate using the quantum Ising model and a recently proposed generalization thereof due to O’Brien and Fendley [Phys. Rev. Lett. 120, 206403]. (i) From the spectrum of low energies and momenta we extract conformal data (specifying the emergent CFT) with unprecedented numerical accuracy. (ii) By changing the lattice size, we investigate nonperturbatively the renormalization group flow of the low-energy spectrum between two CFTs. In our example, where the flow is from the tricritical Ising CFT to the Ising CFT, we obtain excellent agreement with an analytical result [Klassen and Melzer, Nucl. Phys. B370, 51110.1016/0550-3213(92)90422-8] conjectured to describe the flow of the first spectral gap directly in the continuum.

Note:

4 pages, 4 figures, 1 table, plus supplemental material. New model, improved numerics, new comparison of RG flow to field theory result. Code available at https://github.com/FuTen/puMPS.jl

General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
renormalization group: flow
spin: chain
energy: low
field theory: conformal
energy-momentum: spectrum
excited state: energy
Hamiltonian
lattice
ground state

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