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Title: Boundary quantum critical phenomena with entanglement renormalization

Abstract

We propose the use of entanglement renormalization techniques to study boundary critical phenomena on a lattice system. The multiscale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the MERA, an accurate approximation to the ground state of a semi-infinite critical chain with an open boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. As in Wilson's renormalization-group formulation of the Kondo problem, our construction produces, as a side result, an effective chain displaying explicit separation of energy scales. We present benchmark results for the quantum Ising and quantum XX models with free and fixed boundary conditions.

Authors:
; ; ; ;  [1]; ;  [2]
  1. School of Physical Sciences, University of Queensland, Queensland 4072 (Australia)
  2. Depto. Estructura i Constituents de la Materia, Universitat Barcelona, 08028 Barcelona (Spain)
Publication Date:
OSTI Identifier:
21421463
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 82; Journal Issue: 16; Other Information: DOI: 10.1103/PhysRevB.82.161107; (c) 2010 The American Physical Society; Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; BENCHMARKS; BOUNDARY CONDITIONS; GROUND STATES; ISING MODEL; KONDO EFFECT; QUANTUM ENTANGLEMENT; RENORMALIZATION; SCALING; SIMULATION; CALCULATION METHODS; CRYSTAL MODELS; ENERGY LEVELS; MATHEMATICAL MODELS

Citation Formats

Evenbly, G, Pfeifer, R N. C., Tagliacozzo, L, McCulloch, I P, Vidal, G, Pico, V, and Iblisdir, S. Boundary quantum critical phenomena with entanglement renormalization. United States: N. p., 2010. Web. doi:10.1103/PHYSREVB.82.161107.
Evenbly, G, Pfeifer, R N. C., Tagliacozzo, L, McCulloch, I P, Vidal, G, Pico, V, & Iblisdir, S. Boundary quantum critical phenomena with entanglement renormalization. United States. https://doi.org/10.1103/PHYSREVB.82.161107
Evenbly, G, Pfeifer, R N. C., Tagliacozzo, L, McCulloch, I P, Vidal, G, Pico, V, and Iblisdir, S. 2010. "Boundary quantum critical phenomena with entanglement renormalization". United States. https://doi.org/10.1103/PHYSREVB.82.161107.
@article{osti_21421463,
title = {Boundary quantum critical phenomena with entanglement renormalization},
author = {Evenbly, G and Pfeifer, R N. C. and Tagliacozzo, L and McCulloch, I P and Vidal, G and Pico, V and Iblisdir, S},
abstractNote = {We propose the use of entanglement renormalization techniques to study boundary critical phenomena on a lattice system. The multiscale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the MERA, an accurate approximation to the ground state of a semi-infinite critical chain with an open boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. As in Wilson's renormalization-group formulation of the Kondo problem, our construction produces, as a side result, an effective chain displaying explicit separation of energy scales. We present benchmark results for the quantum Ising and quantum XX models with free and fixed boundary conditions.},
doi = {10.1103/PHYSREVB.82.161107},
url = {https://www.osti.gov/biblio/21421463}, journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 16,
volume = 82,
place = {United States},
year = {2010},
month = {10}
}