Effective description of correlations for states obtained from conformal field theory

Benedikt Herwerth, Germán Sierra, J. Ignacio Cirac, and Anne E. B. Nielsen
Phys. Rev. B 96, 115139 – Published 20 September 2017
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Abstract

We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for XXZ spin chains, and they are similar to lattice Laughlin states in two dimensions. We show that their zz correlations are determined by a modification of the original free-boson theory. An expansion to quadratic order leads to a solvable, effective theory for the correlations in these states. Compared to the massless boson, there is an additional term in this effective theory that explains the behavior of the correlations: a polynomial decay in one dimension and at the edge of a two-dimensional system and an exponential decay in the bulk of a two-dimensional system. We test the validity of our approximation by comparing it to Monte Carlo computations.

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  • Received 21 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.115139

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Benedikt Herwerth1,*, Germán Sierra2, J. Ignacio Cirac1, and Anne E. B. Nielsen3,1,4

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
  • 2Instituto de Física Teórica, UAM-CSIC, Madrid, Spain
  • 3Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
  • 4Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark

  • *benedikt.herwerth@mpq.mpg.de

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Issue

Vol. 96, Iss. 11 — 15 September 2017

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