Publication

Realization of higher Wess-Zumino-Witten models in spin chains

Frédéric Mila, Salvatore Manmana, Frédéric Alexis Michaud
2013
Journal paper

Abstract

Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (Si-1 . S-i)(S-i . Si+1) + H.c., we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S = 1, 3/2, and 2. The resulting central charge and critical exponent are in good agreement with the SU(2)(k=2S) Wess-Zumino-Witten values c = 3k/(2 + k) and eta = 3/(2 + k). Since the three-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU(2)(k>1) Wess-Zumino-Witten models might finally be realized in actual spin chains.

Official source

https://infoscience.epfl.ch/record/188850?ln=en

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Ontological neighbourhood

Physics

Thermodynamics: Critical phenomena

Related concepts (29)

Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.

In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking.

This article lists the critical exponents of the ferromagnetic transition in the Ising model. In statistical physics, the Ising model is the simplest system exhibiting a continuous phase transition with a scalar order parameter and symmetry. The critical exponents of the transition are universal values and characterize the singular properties of physical quantities. The ferromagnetic transition of the Ising model establishes an important universality class, which contains a variety of phase transitions as different as ferromagnetism close to the Curie point and critical opalescence of liquid near its critical point.

Related publications (42)

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Realization of higher Wess-Zumino-Witten models in spin chains

Graph Chatbot

Chat with Graph Search

Eight-vertex criticality in the interacting Kitaev chain

Infinitesimal asphericity changes the universality of the jamming transition

Carving out OPE space and precise O(2) model critical exponents

Carving out OPE space and precise O(2) model critical exponents

Infinitesimal asphericity changes the universality of the jamming transition

Eight-vertex criticality in the interacting Kitaev chain