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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Random matrix theory and critical phenomena in quantum spin chains.

J Hutchinson1, J P Keating1, F Mezzadri1

  • 1School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
PubMed
Summary
This summary is machine-generated.

This study analyzes quantum spin chains, calculating critical exponents and ground state correlators. The findings reveal quasi-long-range order and establish exponent universality for these systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • Quantum spin chains are fundamental models in condensed matter physics.
  • Understanding their critical properties is key to classifying phases of matter.
  • Exact solutions are often limited to specific symmetries.

Purpose of the Study:

  • To compute critical properties of a general class of quantum spin chains.
  • To calculate critical exponents (s, ν, z) and ground state correlators.
  • To establish the universality of these exponents under specific symmetry constraints.

Main Methods:

  • Utilizing exact solution techniques for quantum spin chains.
  • Applying symmetry constraints related to classical compact groups (U(N), O(N), Sp(2N)).
  • Calculating critical exponents and ground state correlation functions.

Main Results:

  • Computed critical exponents s (energy gap), ν (correlation length), and z (dynamic exponent).
  • Calculated ground state correlators, showing quasi-long-range order.
  • Demonstrated that critical exponents depend on system parameters.

Conclusions:

  • The study establishes universality of critical exponents for the analyzed class of quantum spin chains.
  • The findings contribute to the understanding of quantum phase transitions.
  • The methods provide a framework for analyzing similar complex quantum systems.