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Equilibrium States, Phase Transitions and Dynamics in Quantum Anharmonic Crystals

Yuri V. Kozitsky

arXiv:1806.08264Springer proceedings in mathematics & statisticsJan 1, 20180 citations

Quantum critical fluctuations in an anharmonic crystal model

André F. Verbeure, Valentin Anatol'evich Zagrebnov

Reports on Mathematical PhysicsAug 1, 19935 citations

On the class of exactly soluble models of phase transitions

Andrzej Radosz

Physics Letters AMar 1, 19900 citations

Finite-size effects in a quantum exactly soluble model for structural phase transition

N. S. Tonchev

Physica A Statistical Mechanics and its ApplicationsFeb 1, 19885 citations

Boson Expansions for an Exactly Soluble Model of Interacting Fermions with SU(3) Symmetry

Shou Yung Li, Abraham Klein, R. M. Dreizler

An exactly soluble three-level model for a system of fermions with Hamiltonian formed from generators of the group SU(3) is studied. A basis for the representation of which the ground state is a member is constructed. It is demonstrated that in this representation, the generators can each be expanded in a series as functions of a pair of ``kinematical'' boson operators; the series are uniquely determined to satisfy the operator algebra and the invariants of the representation by a method of Marumori. It is seen that the lowest anharmonic approximation to the Hamiltonian and other operators yields excellent numerical agreement with exact results for all regimes of interaction strength considered. An alternative description of the system in terms of a dynamically more meaningful boson, called the ``physical'' boson, is shown to be appropriate for relatively weak coupling where one has a near harmonic spectrum.An exactly soluble three-level model for a system of fermions with Hamiltonian formed from generators of the group SU(3) is studied. A basis for the representation of which the ground state is a member is constructed. It is demonstrated that in this representation, the generators can each be expanded in a series as functions of a pair of ``kinematical'' boson operators; the series are uniquely determined to satisfy the operator algebra and the invariants of the representation by a method of Marumori. It is seen that the lowest anharmonic approximation to the Hamiltonian and other operators yields excellent numerical agreement with exact results for all regimes of interaction strength considered. An alternative description of the system in terms of a dynamically more meaningful boson, called the ``physical'' boson, is shown to be appropriate for relatively weak coupling where one has a near harmonic spectrum.

Journal of Mathematical PhysicsMar 1, 197081 citations

On the low-temperature behavior of the critical specific heat capacity of an anharmonic crystal with long-range interaction

Ekaterina S. Pisanova, Angel Y. Krushkov

An exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction (decreasing at large distances r as r−d−σ, where d is the space dimensionality and 0 < σ ≤ 2) is considered near to its zero-temperature critical point. The low-temperature behavior of the bulk specific heat capacity at the lower classical critical dimension (d = σ) is studied in different regions of the (T, λ)-phase diagram, where T is the temperature and λ is a parameter which switches on quantum fluctuations. From the results obtained one can see that when T → 0+ the specific heat capacity tends to zero in a different way in the regions: (a) renormalized classical region - as T raised to the second power and (b) quantum disordered region - exponentially.An exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction (decreasing at large distances r as r−d−σ, where d is the space dimensionality and 0 < σ ≤ 2) is considered near to its zero-temperature critical point. The low-temperature behavior of the bulk specific heat capacity at the lower classical critical dimension (d = σ) is studied in different regions of the (T, λ)-phase diagram, where T is the temperature and λ is a parameter which switches on quantum fluctuations. From the results obtained one can see that when T → 0+ the specific heat capacity tends to zero in a different way in the regions: (a) renormalized classical region - as T raised to the second power and (b) quantum disordered region - exponentially.

AIP conference proceedingsJan 1, 20160 citations

Phase transitions and algebra of fluctuation operators in an exactly soluble model of a quantum anharmonic crystal

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