Quantum Transfer Matrix Method Research Articles

A microscopic study of spin-polarized 40K atoms in one dimension using the static fluctuation approximation (SFA)

The thermodynamic and magnetic properties of a spin-mixture of 40K atoms in a 1D harmonic trap, in the presence of an external magnetic field H, are studied using the static fluctuation approximation (SFA). The two-body interaction used is the contact potential. The thermodynamic properties include the chemical potential, energy per particle, specific heat capacity, and entropy per particle. The magnetic properties comprise the magnetization per particle and susceptibility per particle. A phase transition is observed for the repulsive interactions around 0.35TF and 0.5TF in the channels {–9/2, –7/2} and {–9/2, –5/2}, respectively. A peak appears in the entropy and susceptibility at effective scattering length |a1d| ≈ 0.16 μm. For the attractive interactions, three different behaviors depending on H are found in the low-temperature limit. The first behavior is when H < Hc, where Hc is the critical magnetic field, and typical peaks emerge. The second behavior is at H = Hc, and a magnetic phase transition occurs. The third behavior is when H > Hc and the system becomes a partially polarized phase. Our results are consistent with the reported results obtained by the local density approximation, thermal Bethe ansatz method, mean-field approximation, and quantum transfer matrix method.

Electronic transport in two-dimensional strained Dirac materials under multi-step Fermi velocity barrier: transfer matrix method for supersymmetric systems

In recent years, graphene and other two-dimensional Dirac materials like silicene, germanene, etc. have been studied from different points of view: from mathematical physics, condensed matter physics to high energy physics. In this study, we utilize both supersymmetric quantum mechanics (SUSY-QM) and transfer matrix method (TTM) to examine electronic transport in two-dimensional Dirac materials under the influences of multi-step deformation as well as multi-step Fermi velocity barrier. The effects of multi-step effective mass and multi-step applied fields are also taken into account in our investigation. Results show the possibility of modulating the Klein tunneling of Dirac electron using strain or electric field.

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

We investigate the one-dimensional mixture of scalar bosons and spin polarized fermions interacting through a $\delta$-function potential. Using a thermodynamic description derived by employing a lattice embedding of the continuum model and the quantum transfer matrix method we perform a detailed analysis of the contact and quantum critical behaviour. We show that the compressibility Wilson ratio presents anomalous enhancement at the quantum critical points and that the boundaries of the quantum critical regions can be well mapped by the maxima of the specific heat. As a function of the coupling strength and temperature the contact presents nonmonotonic behavior. In the strong coupling regime the local minimum exhibited by the contact as a function of temperature is accompanied by a significant momentum reconstruction at both low and high momenta. This momentum reconstruction occurs as the system crosses the boundary between the Tomonaga-Luttinger liquid phase to the spin-incoherent regime and provides an experimental signature of the transition.

A TBA approach to thermal transport in the XXZ Heisenberg model

We show that the thermal Drude weight and magnetothermal coefficient of the 1D easy-plane Heisenberg model can be evaluated by an extension of the Bethe ansatz thermodynamics formulation by Takahashi and Suzuki (1972 Prog. Theor. Phys. 48 2187). They have earlier been obtained by the quantum transfer matrix method (Klümper 1999 Z. Phys. B 91 507). Furthermore, this approach can be applied to the study of the far-out of equilibrium energy current generated at the interface between two semi-infinite chains held at different temperatures.

Exact thermodynamics and phase diagram of integrable t-J model with chiral interaction

We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose, we apply the quantum transfer matrix method which results in a finite set of non-linear integral equations. We obtain numerical solutions to these equations leading to results for thermodynamic quantities as a function of temperature, magnetic field, particle density and staggering parameter. Studying the maxima lines of entropy at low but non zero temperature reveals the phase diagram of the model. There are ten different phases which we may classify in terms of the qualitative behaviour of auxiliary functions, closely related to the dressed energy functions.

A Riemann-Hilbert formulation for the finite temperature Hubbard model

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Juttner, Klumper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

Long-distance behavior of temperature correlation functions in the one-dimensional Bosegas

We describe a Bethe ansatz-based method to derive, starting from a multiple integralrepresentation, the long-distance asymptotic behavior at finite temperature of thedensity–density correlation function in the interacting one-dimensional Bose gas. Wecompute the correlation lengths in terms of solutions of non-linear integral equations of thethermodynamic Bethe ansatz type. Finally, we establish a connection between the resultsobtained in our approach and the correlation lengths stemming from the quantum transfermatrix method.

Quantum Transfer Matrix Approach to Dynamical Correlation Functions for the Transverse Ising Chain

The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is applied to dynamical problems. The autocorrelation functions of the Transverse Ising chain are derived by this method as an example. The Trotter-directional correlation functions are interpreted as a Matsubara’s temperature Green function, so that the analytic continuation of the Green functions yields the desired autocorrelation functions. Subject Index: 040, 043, 046, 070, 370

Fractality of Hofstadter Butterfly in Specific Heat Oscillation

We calculate thermodynamical properties of the Hofstadter model using a recently developed quantum transfer matrix method. We find intrinsic oscillation features in specific heat that manifest the fractal structure of the Hofstadter butterfly. We also propose experimental approaches which use specific heat as an access to detect the Hofstadter butterfly.

A quantum transfer matrix method for one-dimensional disordered electronicsystems

We develop a novel quantum transfer matrix method to study thermodynamicproperties of one-dimensional (1D) disordered electronic systems. It isshown that the partition function can be expressed as a product of2 × 2 local transfer matrices. We demonstrate this method by applying it to the 1D disorderedAnderson model. Thermodynamic quantities of this model are calculated and discussed.

Probing the Hofstadter butterfly with the quantum oscillation of magnetization

We have developed a different quantum transfer-matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haas--van Alphen oscillation of magnetization bears the energy structure of the Hofstadter butterfly. The measurement of this quantum correction, which can be materialized on the superlattice or cold atom systems, can reveal unambiguously the Hofstadter fractal energy spectrum.

Specific heat study of quasi-one-dimensional antiferromagnetic model for an organic polymer chain

The specific heat of an infinite one-dimensional polymer chain bearing periodically arranged side radicals connected to the even sites is studied by means of quantum transfer-matrix method based on a Ising–Heisenberg model. In the absence of the exchange interactions between side radicals and the main chain, the curves of specific heat show a round peak due to the antiferromagnetic excitations for the all antiferromagnetic interactions along the polymer chain. Considering the exchange interactions between the side radicals and the main chain, the curves of the specific heat show double-peak structure for ferromagnetic interactions between the radicals and main chain, indicating that a competition between ferromagnetic and antiferromagnetic interactions and the possibility of the occurrence of the stable ferrimagnetic state along the polymer chain.

Field-dependent specific-heat of the pure and diluted 4f electron system Yb 4As 3

The experimental field-dependent specific heat of the polydomain pure Yb 4As 3 and diluted (Yb 1− x Lu x ) 4As 3 ( x = 0.01, 0.03) systems is presented and compared with that calculated by the numerical quantum transfer-matrix method. The simulations have been performed using the S = 1/2 antiferromagnetic Heisenberg model with the transverse staggered field (appearing as a result of the antisymmetric Dzyaloshinskii–Moriya interaction) and a uniform magnetic field perpendicular to the staggered field. In the model calculations the fixed microscopic parameters have been taken and the impurity distribution has been considered. A significant improvement with respect to the previous results is shown.

Finite-Temperature Phase Transitions in Quasi-One-Dimensional Molecular Conductors

Phase transitions in 1/4-filled quasi-one-dimensional molecular conductors are studied theoretically on the basis of extended Hubbard chains including electron-lattice interactions coupled by interchain Coulomb repulsion. We apply the numerical quantum transfer-matrix method to an effective one-dimensional model, treating the interchain term within mean-field approximation. Finite-temperature properties are investigated for the charge ordering, the "dimer Mott" transition (bond dimerization), and the spin-Peierls transition (bond tetramerization). A coexistent state of charge order and bond dimerization exhibiting dielectricity is predicted in a certain parameter range, even when intrinsic dimerization is absent.

Phase Transitions in Spin-orbital Coupled Model for Pyroxene Titanium Oxides

We study the competing phases and the phase transition phenomena in an effective spin-orbital coupled model derived for pyroxene titanium oxides ATiSi2O6 (A=Na, Li). Using the mean-field-type analysis and the numerical quantum transfer matrix method, we show that the model exhibits two different ordered states, the spin-dimer and orbital-ferro state and the spin-ferro and orbital-antiferro state. The transition between two phases is driven by the relative strength of the Hund's-rule coupling to the onsite Coulomb repulsion and/or by the external magnetic field. The ground-state phase diagram is determined. There is a keen competition between orbital and spin degrees of freedom in the multicritical regime, which causes large fluctuations and significantly affects finite-temperature properties in the paramagnetic phase.

Field-dependent specific heat and magnetization for the [formula omitted] antiferromagnetic chain Yb4As3: simulation and experiments

The S=12 antiferromagnetic Heisenberg model with the transverse staggered field and uniform magnetic field perpendicular to the staggered field is applied to the semimetallic compound Yb4As3. The field-dependent specific heat for infinite and finite chains as well as the magnetization for infinite chains are calculated by the numerical quantum transfer-matrix method. Specific heat data for polydomain samples of Yb4As3 and (Yb0.99Lu0.01)4As3 at B=12T are presented and compared with numerical results obtained for microscopic parameters taken from theoretical predictions. Magnetization data for single domain and polydomain samples of Yb4As3 are also compared with simulation results.

Thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies

The thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies are investigated via the integrable $su(3)$ model in terms of the quantum transfer matrix method and the recently developed high temperature expansion method for exactly solved models. It is shown that large single-ion anisotropy may result in a singlet gapped phase in the spin-$1$ chain which is significantly different from the standard Haldane phase. A large in-plane anisotropy may destroy the gapped phase. On the other hand, in the vicinity of the critical point a weak in-plane anisotropy leads to a different phase transition than the Pokrovsky-Talapov transition. The magnetic susceptibility, specific heat, and magnetization evaluated from the free energy are in excellent agreement with the experimental data for the compounds ${\mathrm{Ni}(\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}$ and ${\mathrm{Ni}(\mathrm{C}}_{10}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$.

Quantum Monte Carlo study on commensurate–incommensurate transition in the spin-1/2 XXZ chain at finite temperatures

A crossover phenomenon of the longitudinal spin–spin correlation function is investigated on the spin-1/2 XXZ chain in a magnetic field at finite temperatures. A commensurate–incommensurate transition of the correlation function in the asymptotic behaviour has been pointed out by Klumper et al in the framework of the quantum transfer matrix method. We show the field dependence and the anisotropy-constant dependence of the critical temperature by the quantum transfer matrix method. Using a quantum Monte Carlo method with the continuous time loop algorithm, we directly observe the commensurate–incommensurate transition. Detailed quantum Monte Carlo analyses for the longitudinal spin–spin correlation in both the high and low temperature regions are presented. Especially in the low temperature region, evaluating the precise distance dependence of the correlation function, we prove that the incommensurate oscillation has detectable amplitude, which has not been estimated before. We also estimate the phase factor of the incommensurate oscillation, which accurately coincides with the one from the quantum transfer matrix method.

Antiferromagnetic interactions in the semimetallic Yb 4As 3: field-dependent specific heat and magnetization data

The S= 1 2 antiferromagnetic Heisenberg model with the Dzyaloshinsky–Moriya interaction is applied to a semimetallic compound Yb 4As 3. The field dependent specific heat and the magnetization of this model are calculated by the numerical quantum transfer-matrix method and compared with experiment. New specific heat experimental results for the polydomain sample in the field applied are presented and compared with the theoretical predictions obtained without adjustable microscopic parameters.

Exact results for the thermal and magnetic properties of strong coupling ladder compounds.

We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy, and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP)2CuBr4.2H(2)O, Cu2(C5H12N2)2Cl4, etc.