Asymptotic expansion of the ground state energy of half-filled Hubbard model
This paper was withdrawn by the author because the results already appeared in PRB 20, 4756 (1979).
cond-mat↗
arXiv subjects
Minoru Takahashi
Publications and source records attributed to Minoru Takahashi.
Magnetization plateau in S=3/2 antiferromagnetic Heisenberg chain with anisotropy
The magnetization process of the S=3/2 antiferromagnetic Heisenberg chain with the single-ion anisotropy D at T=0 is investigated by the exact diagonalization of finite clusters and finite-size scaling analyses. It is found that a magnetization plateau appears at m=1/2 for $D>D_c=0.93 \pm 0.01$. The phase transition with respect to D at D_c is revealed to be the Kosterlitz-Thouless-type. The magnetization curve of the infinite system is also presented for some values of D.
cond-mat.stat-mech↗
Three-leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties
The antiferromagnetic Heisenberg spin systems on the three-leg ladder are investigated. Periodic boundary condition is imposed in the rung direction. The system has an excitation gap for all antiferromagnetic inter-chain coupling ($J_{\perp}>0$). The estimated gap for the strong coupling limit ($J_{\perp}/J_1 \to \infty$) is 0.28$J_1$. Although the interaction is homogeneous and only nearest-neighbor, the ground states of the system are dimerized and break the translational symmetry in the thermodynamic limit. Introducing the next-nearest neighbor coupling ($J_2$), we can see that the system is solved exactly. The ground state wave function is completely dimer-ordered. Using density matrix renomalization group algorithm, we show numerically that the original model ($J_2=0$) has the same nature with the exactly solvable model. The ground state properties of the ladder with a higher odd number of legs are also discussed.
cond-mat.stat-mech↗
Low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond-alternation
We investigate the low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond-alternation by the quantum Monte Carlo method (loop algorithm). The strength of bond-alternation at the gapless point is estimated as $δ_{c}=0.2595\pm0.0005$. We confirm numerically that the low-temperature properties at the gapless point are consistent with field theoretical predictions. The numerical results are compared with those of the spin-1/2 antiferromagnetic Heisenberg chain and recent experimental results for [\{Ni(333-tet)($μ$-N$_3$)\}$_n$](ClO$_4$)$_n$ (333-tet=tetraamine $N,N^{\prime}$-bis(3-aminopropyl)-1,3-propanediamine).
cond-mat.stat-mech↗
Thermodynamical Bethe Ansatz and Condensed Matter
The basics of the thermodynamic Bethe ansatz equation are given. The simplest case is repulsive delta function bosons, the thermodynamic equation contains only one unknown function. We also treat the XXX model with spin 1/2 and the XXZ model and the XYZ model. This method is very useful for the investigation of the low temperature thermodynamics of solvable systems.
cond-mat.stat-mech↗
Magnetization process of the spin-1/2 XXZ models on square and cubic lattices
The magnetization process of the spin-1/2 antiferromagnetic XXZ model with Ising-like anisotropy in the ground state is investigated. We show numerically that the Ising-like XXZ models on square and cubic lattices show a first-order phase transition at some critical magnetic field. We estimate the value of the critical field and the magnetization jump on the basis of the Maxwell construction. The magnetization jump in the Ising-limit is investigated by means of perturbation theory. Based on our numerical results, we briefly discuss the phase diagram of the extended Bose-Hubbard model in the hard-core limit.
cond-mat.stat-mech↗
Universal low-temperature properties of quantum and classical ferromagnetic chains
We identify the critical theory controlling the universal, low temperature, macroscopic properties of both quantum and classical ferromagnetic chains. The theory is the quantum mechanics of a single rotor. The mapping leads to an efficient method for computing scaling functions to high accuracy.
cond-mat↗
Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field. II
The finite-size scaling function of the nonlinear susceptibility of the ferromagnetic Heisenberg chain is given explicitly. It is conjectured that the scaling function is universal for any values of $S$. The conjecture is based on the exact solution of the nonlinear susceptibility for $S=\infty$, and numerical calculations for $S=1/2$ and $S=1$.
cond-mat↗
Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions
Quantum Heisenberg ferromagnets with long-range interactions decayin as $1/r^p$ in one and two dimensions are investigated by means of the Green's function method. It is shown that there exists a finite-temperature phase transition in the region $d<p<2 d$ for the $d$-dimensional case and that no transitions at any finite temperature exist for $p\ge 2 d$; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on $p$; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.
cond-mat↗
Fine Structure and Fractional Aharonov-Bohm Effect
We find a fine structure in the Aharonov-Bohm effect, characterized by the appearence of a new type of periodic oscillations having smaller fractional period and an amplitude, which may compare with the amplitude of the conventional Aharonov-Bohm effect. Specifically, at low density or strong coupling on a Hubbard ring can coexist along with the conventional Aaronov-Bohm oscillations with the period equal to an integer, measured in units of the elementary flux quantum, two additional oscillations with periods $1/N$ and $M/N$. The integers $N$ and $M$ are the particles number and the number of down-spin particles, respectively. {}From a solution of the Bethe ansatz equations for $N$ electrons located on a ring in a magnetic field we show that the fine structure is due to electron-electron and Zeeman interactions. Our results are valid in the dilute density limit and for an arbitrary value of the Hubbard repulsion $U$
cond-mat↗
Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
Highly accurate results are presented for the susceptibility, $χ(T)$ of the $s=1/2$ Heisenberg antiferromagnetic chain for all temperatures, using the Bethe ansatz and field theory methods. After going through a rounded peak, $χ(T)$ approaches its asympotic zero-temperature value with infinite slope.
cond-mat↗
Excitation Spectrum of $S=1$ Antiferromagnetic Chains
The dynamical structure factor $S(Q,ω)$ of the $S=1$ antiferromagnetic Heisenberg chain with length 20 at zero temperature is calculated. The lowest energy states have the delta-function peak at the region $π\ge \vert Q\vert >0.3π$. At $\vert Q\vert<0.3π$ the lowest energy states are the lower-edge of the continuum of the scattering state, the strength of which decreases for large systems. This gives a reasonable explanation for the experimental fact that no clear peak is observed at the region $Q<0.3π$. This situation is more apparent for valence-bond solid state. On the contrary for $S=1/2$ antiferromagnetic Heisenberg chain the lowest energy states are always the edge of the continuum.
cond-mat↗
Strong-Correlations Versus U-Center Pairing and Fractional Aharonov-Bohm Effect
The influence of the interaction between electrons on the Aharonov-Bohm effect is investigated in the framework of the Hubbard model. The repulsion between electrons associated with strong correlation is compared with the case of attraction such as $U$-center pairing. The most interesting case, when two electrons are located on a ring, is investigated in detail using the Bethe ansatz method and by exact numerical diagonalization of the Hubbard hamiltonian. It is shown that the quasi half quantum flux periodicity occurs for any nonzero values of $U$. For large number of sites, or strong U, the quasi periodicity becomes an exact half quantum flux periodicity. However the character of the state created on the ring is different in both cases. In the case of $U$-center pairing the electrons are bound in pairs located on the same site. For strong correlations(large positive $ U$) the electrons tend to be far from each other as possible. We show by numerical solution of Bethe ansaz equations that for three electrons the flux periodicity of the ground state energy is equal to 1/3. The one third periodicity may occur even for small values of the ratio $U/t$, for the very dilute system. It is shown analytically using the Bethe ansaz equations for $N$ electrons, that for dilute systems with arbitrary value of the Hubbard repulsion $U$,
cond-mat↗
Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature
A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition in the region where the model has longer-range interactions than the HS model. The critical temperature is estimated.
cond-mat↗