Quantum Monte Carlo study of symmetry breaking in a double-well chain

Conference · Tue Jan 01 00:00:00 EST 1991

DOI:https://doi.org/10.1007/978-1-4615-3466-2_30· OSTI ID:5373461

Gubernatis, J E; Campbell, D K; Wang, Xidi

We report the results of a quantum Monte Carlo simulation of a double-well chain. This chain is a system of particles that move on a lattice of symmetric, double-well potentials which are coupled harmonically to one another. The physical properties of this system are invariant, like those of the Ising model, under the symmetry operations of the Z{sub 2} group. In this case, changing the sign of the displacement variables leaves the energy unchanged and leads to a doubly-degenerate ground-state. Classically, this symmetry is always broken, and the particles all sit in the left- or the right-hand side of their wells. Quantum mechanically, however, we find that below a critical value of the double-well coupling constant the symmetry is restored by quantum fluctuations. Our interest in this model was motivated by a series of quantum Monte Carlo simulations we are performing on one-dimensional models of conducting polymers and synthetic metals. The properties of these materials are described by a system of interacting electrons coupled to a system of phonons. Several years ago, for similar models, Fradkin and Hirsch investigated how the electron motion can generate an effective double-well potential for the phonons and thereby cause the lattice to dimerize. They also argued, based on continuum renormalization group considerations and quantum Monte Carlo simulations, that for certain models quantum fluctuations at low temperatures restore symmetry (i.e., destroy the dimerization). We were attracted to the quantum double-well chain because it is a simpler problem than the electron-phonon models on which to test new numerical methods and to study similar issues.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5373461
• Report Number(s): LA-UR-91-2731; CONF-9108142-1; ON: DE91018032
• Resource Relation: Conference: Recent progress in many-body theories, Minneapolis, MN (United States), 26-31 Aug 1991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
POTENTIALS
SYMMETRY BREAKING
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
HARMONIC OSCILLATORS
MONTE CARLO METHOD
PHASE DIAGRAMS
SPECIFIC HEAT
DIAGRAMS
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
MATHEMATICAL OPERATORS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
QUANTUM OPERATORS
THERMODYNAMIC PROPERTIES
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics