A Non-unitary Mapping from Cooper Pairs to Bosons

We derive a non-hermitian boson-fermion Hamiltonian, that is equivalent to the entirely fermionic Richardson Hamiltonian which describes the dynamics of conduction electrons in a superconductor. This is done using a generalized Dyson mapping, that replaces Cooper pairs with bosons. We show that the calculation of some physical quantities is simpler when one uses the boson-fermion Hamiltonian rather than the original Richardson Hamiltonian.     

Modified factorization method and supersymmetric quantum mechanics

We suggest a modified factorization scheme within a supersymmetric framework which affords a consistent treatment of a wide class of Schrödinger potentials. A consequence of this is the possibility of deriving a boson-fermion Hamiltonian with linear interaction.     

Hot and cold denaturation of proteins: Critical aspects

We argue that the first order hot and cold folding transitions of proteins observed at physiological chemical conditions ends in a critical point at a given temperature and chemical potential of the surrounding water. We investigate the properties of this critical point using a single-pathway scenario for the folding process. This pathway assumption determines the form of a Hamiltonian whose critical properties define a new universality class. Received 9 November 1998     

Effects of single particle on shape phase transitions and phase coexistence in odd-even nuclei

A classical analysis of shape phase transitions and phase coexistence in odd-even nuclei has been performed in the framework of the interacting boson-fermion model. The results indicate that the effects of a single particle may influence different types of transitions in different ways. Especially, it is revealed that phase coexistence can clearly emerge in the critical region and thus be taken as a indicator of the shape phase transitions in odd-even nuclei.     

Dynamic Phase Transitions and Compensation Temperatures in a Mixed Spin-3/2 and Spin-5/2 Ising System

We examine the dynamic phase transitions and the dynamic compensation temperatures, within a mean-field approach, in the mixed spin-3/2 and spin-5/2 Ising system with a crystal-field interaction under a time-varying magnetic field on a hexagonal lattice by using Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices with σ=3/2 and S=5/2. The Hamiltonian model includes intersublattice, intrasublattice, and crystal-field interactions. The intersublattice interaction is considered antiferromagnetic and to be a simple but interesting model of a ferrimagnetic system. We employ the Glauber transition rates to construct the mean-field dynamic equations, and we solve these equations in order to find the phases in the system. We also investigate the thermal behavior of the dynamic sublattice magnetizations and the dynamic total magnetization to obtain the dynamic phase transition points and compensation temperatures as well as to characterize the nature (continuous and discontinuous) of transitions. We also calculate the dynamic phase diagrams including the compensation temperatures in five different planes. According to the values of Hamiltonian parameters, five different fundamental phases, three different mixed phases, and six different types of compensation behaviors in the Néel classification nomenclature exist in the system.     

Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

The Binding Energy, Spin－Excitation Gap, and Charged Gap in the Boson－Fermion Model

In this paper, by applying a simplified version of Lieb‘s spin-reflection-positivity method, which was recently developed by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some general properties of the boeon-fermion Hamiltonlan, which has been widely used as a phenomenological model to describe the real-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive couping V, which represents the spontaneous decay and recombination process between boson and fermion in the model, the pairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermion Hamiltonian is always larger than its charged gap, as predicted by the pre-palred electron theory.     

Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.     

On $\mathsf{c = 1}$ critical phases in anisotropic spin-1 chains

Quantum spin-1 chains may develop massless phases in presence of Ising-like and single-ion anisotropies. We have studied c = 1 critical phases by means of both analytical techniques, including a mapping of the lattice Hamiltonian onto an O(2) NL M, and a multi-target DMRG algorithm which allows for accurate calculation of excited states. We find excellent quantitative agreement with the theoretical predictions and conclude that a pure Gaussian model, without any orbifold construction, describes correctly the low-energy physics of these critical phases. This combined analysis indicates that the multicritical point at large single-ion anisotropy does not belong to the same universality class as the Takhtajan-Babujian Hamiltonian as claimed in the past. A link between string-order correlation functions and twisting vertex operators, along the c = 1 line that ends at this point, is also suggested.Received: 16 July 2003, Published online: 24 October 2003PACS: 75.40.-s Critical-point effects, specific heats, short-range order - 75.10.Jm Quantized spin models - 02.70.-c Computational techniques     

Picturing quantum phase transitions

We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlations in the vicinity of the critical points are analyzed both in the ground states and low temperature thermal states.     

Entanglement of fermions at quantum criticality

The study of entanglement properties of quantum critical many-particle systems has become a subject of intense interest. While the basic features of entanglement scaling for critical spin-1/2 systems (coupled qubits) are by now fairly well understood, entanglement properties of critical fermions (or bosons) are less well studied. In an effort to contribute to this problem, we have analyzed the single-site entanglement of a generic spin-1/2 lattice fermion system and found that (under certain provisos) this measure can be used as a reliable marker to identify and partly characterize a quantum critical point. We illustrate our findings by exact analytical results for the single-site entanglement at the magnetic and Mott-Hubbard transitions of the 1D Hubbard model and at the Mott-Hubbard transitions of the 1D Hubbard model with long-range hopping. The text was submitted by the authors in English.     

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

Exceptional points of a Hamiltonian and phase transitions in finite systems

For a model Hamiltonian which describesN interacting Fermions and which is typical for systems that undergo phase transitions it is shown that for finiteN the transitional point is associated with exceptional points of the Hamiltonian. In the limit of largeN these singularities move down to the real axis. The nature of the limit turns out to be quite different depending on whether it is taken for interaction strengths smaller or larger than the critical value.     

Finite-temperature scaling of quantum coherence near criticality in a spin chain

We explore quantum coherence, inherited from Wigner-Yanase skew information, to analyzequantum criticality in the anisotropic XY chain model at finite temperature. Based on theexact solutions of the Hamiltonian, the quantum coherence contained in a nearest-neighborspin pairs reduced density matrix ρ is obtained. The first-order derivative of thequantum coherence is non-analytic around the critical point at sufficient low temperature.The finite-temperature scaling behavior and the universality are verified numerically. Inparticular, the quantum coherence can also detect the factorization transition in such amodel at sufficient low temperature. We also show that quantum coherence contained indistant spin pairs can characterize quantum criticality and factorization phenomena atfinite temperature. Our results imply that quantum coherence can serve as an efficientindicator of quantum criticality in such a model and shed considerable light on therelationships between quantum phase transitions and quantum information theory at finitetemperature.     

Diverging thermal expansion of the spin-ladder system (C5H12N)2CuBr4

We present high-resolution measurements of the c(*)-axis thermal expansion and magnetostriction of piperidinium copper bromide (C5H12N)2CuBr4. The experimental data at low temperatures are well accounted for by a two-leg spin-ladder Hamiltonian. The thermal expansion shows a complex behavior with various sign changes and approaches a 1/square root T divergence at the critical fields. All low-temperature features are semiquantitatively explained within a free-fermion model; full quantitative agreement is obtained with quantum Monte Carlo simulations.     

Phase diagrams and magnetic properties of the mixed spin-1 and spin-3/2 Ising ferromagnetic thin film: Monte Carlo treatment

Phase diagrams and magnetic properties of the mixed spin-1 and spin-3/2 Ising film with different single-ion anisotropies are investigated, by the use of Monte Carlo simulation based on heat bath algorithms. The effects of the crystal-fields and the surface coupling on the phase diagrams are investigated in detail and the obtained phase diagrams are presented. Depending on the Hamiltonian parameters, the system exhibits both second-and first-order phase transitions besides tricritical point, triple point, and isolated critical end point.     

Effects of an odd particle on shape phase transitions in odd-even systems

A scheme to solve the Hamiltonian in the interacting boson-fermion model in terms of the SU(3) coupling basis is introduced,through which the effects of an odd particle on shape phase transitions(SPTs) in odd-A nuclei are examined by comparing the critical behaviors of some selected quantities in odd-even and even-even systems.The results indicate that the spherical to prolate(U(5)-SU(3)) SPT and spherical to γ-soft(U(5)-O(6)) SPT may clearly occur in the odd-even system with the SPT signatures revealed by various quantities including the excitation energies,energy ratio,B(E2) ratio,quadrupole moments,and one-particle-transfer spectroscopic intensities.In particular,the results indicate that the spherical to prolate SPT in the odd-even system can even be strengthened by the effects of the odd particle with the large fluctuations of the quadrupole deformations appearing near the critical point.     

Phase transitions and critical indices of a phospholipid bilayer model

A model is described which has been used in theoretical studies of a variety of phenomena (which are briefly summarized) relating to biological membranes. It is shown that the Hamiltonian describing this model can be mapped onto an Ising Hamiltonian with a temperature dependent field. It is also shown that this field varies linearly with temperature in the critical region. Exact solutions of this model are presented and its first and second order transitions are discussed with an emphasis on obtaining its critical indices. General considerations lead to the following relations: β=1/δ, α=γ, α′=γ′, where α, β, γ, δ are the critical indices for the specific heat, magnetization, susceptibility and critical isotherm respectively (the primes denoting low temperature indices). These relations are demonstrated explicitly for the Bethe lattice with coordination numbersq=2 and 6.     

SOLVABLE BOSON-FERMION MODEL FOR MIXED-VALENCE SYSTEMS

Using the Bethe ansatz technique, the exact eigenstates of the Hamiltonian of the boson-fermion model for mixed-valence systems are constructed. The Bethe ansatz equations are obtained from the periodic boundary conditions.