TY - JOUR

T1 - Phase diagram of one-dimensional electron-phonon systems. II. the molecular-crystal model

AU - Hirsch, Jorge E.

AU - Fradkin, Eduardo

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1983

Y1 - 1983

N2 - We study the nature of the ground state of a one-dimensional electron-phonon model for molecular crystals: The phonons are assumed dispersionless and couple to the local electronic density. We consider the half-filled-band sector and discuss the stability of the Peierls-dimerized ground state as a function of the phonon frequency (), electron-phonon coupling constant (), and number of components of the electron spin (n). First, we discuss the properties of the model in the limiting cases of zero frequency and infinite frequency. We then perform a strong coupling expansion which maps the system onto a spinless fermion model with nearest-neighbor repulsion for both spinless and spin- electrons, but with different parameters in both cases. Finally, we perform a numerical study of the system using a Monte Carlo technique. We study the behavior of the order parameter and of correlation functions for various points in parameter space. We also perform a finite-sizescaling analysis of the numerical data. The conclusions of our study are the following: For the case of spinless electrons, there exists always a disordered phase for small coupling constant, and the system undergoes an infinite-order transition to a Peierls-dimerized state as the coupling constant increases beyond a critical value. The phase diagram is divided between a disordered and an ordered region by a line that connects the points (=0, =0) and (=, =). For the case of spin- electrons, the system is dimerized for arbitrary and except in the limit =.

AB - We study the nature of the ground state of a one-dimensional electron-phonon model for molecular crystals: The phonons are assumed dispersionless and couple to the local electronic density. We consider the half-filled-band sector and discuss the stability of the Peierls-dimerized ground state as a function of the phonon frequency (), electron-phonon coupling constant (), and number of components of the electron spin (n). First, we discuss the properties of the model in the limiting cases of zero frequency and infinite frequency. We then perform a strong coupling expansion which maps the system onto a spinless fermion model with nearest-neighbor repulsion for both spinless and spin- electrons, but with different parameters in both cases. Finally, we perform a numerical study of the system using a Monte Carlo technique. We study the behavior of the order parameter and of correlation functions for various points in parameter space. We also perform a finite-sizescaling analysis of the numerical data. The conclusions of our study are the following: For the case of spinless electrons, there exists always a disordered phase for small coupling constant, and the system undergoes an infinite-order transition to a Peierls-dimerized state as the coupling constant increases beyond a critical value. The phase diagram is divided between a disordered and an ordered region by a line that connects the points (=0, =0) and (=, =). For the case of spin- electrons, the system is dimerized for arbitrary and except in the limit =.

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U2 - 10.1103/PhysRevB.27.4302

DO - 10.1103/PhysRevB.27.4302

M3 - Article

AN - SCOPUS:17044417942

VL - 27

SP - 4302

EP - 4316

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 7

ER -