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Masahiro Shiroishi

Publications and source records attributed to Masahiro Shiroishi.

At least 19 recordsLinked to original sources
arXiv2007

Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at $Δ$=1/2

We have analytically obtained all the density matrix elements up to six lattice sites for the spin-1/2 Heisenberg XXZ chain at $Δ=1/2$. We use the multiple integral formula of the correlation function for the massless XXZ chain derived by Jimbo and Miwa. As for the spin-spin correlation functions, we have newly obtained the fourth- and fifth-neighbour transverse correlation functions. We have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. Using these results the exact values of the entanglement entropy for the reduced density matrix up six lattice sites have been obtained. We observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory.

cond-mat.stat-mech↗
arXiv2007

String correlation functions of the spin-1/2 Heisenberg XXZ chain

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.

cond-mat.stat-mech↗
arXiv2006

Exact evaluation of density matrix elements for the Heisenberg chain

We have obtained all the density matrix elements on six lattice sites for the spin-1/2 Heisenberg chain via the algebraic method based on the quantum Knizhnik-Zamolodchikov equations. Several interesting correlation functions, such as chiral correlation functions, dimer-dimer correlation functions, etc... have been analytically evaluated. Furthermore we have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a result the exact von Neumann entropy for the reduced density matrix on six lattice sites has been obtained.

hep-th↗
arXiv2005

Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function

Analytical expressions of some of the spin-spin correlation functions up to eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at zero temperature without magnetic field are obtained. The key object of our method is the generating function of two-point spin-spin correlators, whose functional relations are derived from those for general inhomogeneous correlation functions previously obtained from the quantum Knizhnik-Zamolodchikov equations. We show how the generating functions are fully determined by their functional relations, which leads to the two-point spin-spin correlators. The obtained analytical results are numerically confirmed by the exact diagonalization for finite systems.

hep-th↗
arXiv2005

Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain

We study the generating function of the spin-spin correlation functions in the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without magnetic field. We have found its fundamental functional relations from those for general correlation functions, which originate in the quantum Knizhink-Zamolodchikov equation. Using these relations, we have calculated the explicit form of the generating functions up to n=6. Accordingly we could obtain the spin-spin correlator up to k=5.

hep-th↗
arXiv2005

High temperature expansion of emptiness formation probability for isotropic Heisenberg chain

Recently, Göhmann, Klümper and Seel have derived novel integral formulas for the correlation functions of the spin-1/2 Heisenberg chain at finite temperature. We have found that the high temperature expansion (HTE) technique can be effectively applied to evaluate these integral formulas. Actually, as for the emptiness formation probability ${P(n)}$ of the isotropic Heisenberg chain, we have found a general formula of the HTE for ${P(n)}$ with arbitrary $n \in {\mathbb Z}_{\ge 2}$ up to ${O((J/T)^{4})}$. If we fix a magnetic field to a certain value, we can calculate the HTE to much higher order. For example, the order up to ${O((J/T)^{42})}$ has been achieved in the case of ${P(3)}$ when ${h=0}$. We have compared these HTE results with the data by Quantum Monte Carlo simulations. They exhibit excellent agreements.

cond-mat.stat-mech↗
arXiv2004

Evaluation of Dynamic spin structure factor for the spin-1/2 XXZ chain in a magnetic field

Transition rates and dynamic spin structure factor at zero temperature for the spin-1/2 XXZ chain at critical regime in a magnetic field are numerically evaluated in terms of the exact determinant representations for the form factors and norms of the Bethe eigenstates. We have seen that the transition rates converges toward the constant function with the value 1 in the limit delta -> 0. The observed critical exponent of the singularity at the lower boundary is compared with the one predicted from the comformal field theory. We confirm that they are in good agreement. Further we have discovered that a small peak emerges near the upper boundary in the line shape of S(q,omega) for 0<delta<1.

cond-mat.stat-mech↗
arXiv2004

Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain

The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for -1<Δ\leq 1 and 1<Δ. In particular, adjacent four-point correlation functions were given as certain four-dimensional integrals. We show that these integrals can be reduced to polynomials with respect to specific one-dimensional integrals. The results give the polynomial representation of the third-neighbor correlation functions.

cond-mat.stat-mech↗
arXiv2003

Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region

The correlation functions of the spin-1/2 XXZ spin chain in the ground state are expressed in the form of the multiple integrals. For -1< Delta <1, they were obtained by Jimbo and Miwa in 1996. Especially the next nearest-neighbour correlation functions are given as certain three-dimensional integrals. We shall show these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions. We have also found that the remaining one-dimensinal integrals can be evaluated analytically, when nu = arccos(Delta)/pi is a rational number.

cond-mat.stat-mech↗
arXiv2003

Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet

We exactly evaluate the third neighbor correlator and all the possible non-zero correlators of the spin-1/2 Heisenberg $XXX$ antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.

cond-mat.stat-mech↗
arXiv2002

Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high temperature expansion of the specific heat and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high temperature expansion to the low temperature region.

cond-mat.stat-mech↗
arXiv2001

TBA Equations of 1D Hubbard Model and High-Temperature Expansion

New numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of one-dimensional Hubbard model is numerically calculated and compared with high temperature expansion and numerical results of quantum transfer matrix method by Jüttner, Klümper and Suzuki. The coincidence is surprisingly good. We get high-temperature expansion of grand potential up to $β^6$.

cond-mat.str-el↗
arXiv2001

Emptiness Formation Probability for the One-Dimensional Isotropic XY Model

We study a correlation function for the one-dimensional isotropic ${XY}$ model (${XX0}$ model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.

cond-mat.stat-mech↗
arXiv2001

Equivalence of TBA and QTM

The traditional thermodynamic Bethe ansatz (TBA) equations for the XXZ model at $|Δ|\ge 1$ are derived within the quantum transfer matrix (QTM) method. This provides further evidence of the equivalence of both methods. Most importantly, we derive an integral equation for the free energy formulated for just one unknown function. This integral equation is different in physical and mathematical aspects from the established ones. The single integral equation is analytically continued to the regime $|Δ|<1$.

cond-mat.stat-mech↗
arXiv1999

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $ $ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.

cond-mat.stat-mech↗
arXiv1998

Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.

cond-mat.str-el↗
arXiv1998

Fermionic R-Operator for the Fermion Chain Model

The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of the fermion operators. The R-operator satisfies a new type of the Yang-Baxter relation with fermionic L-operator. We derive the fermionic Sutherland equation from the relation, which is equivalent to the fermionic Lax equation. It also provides a mathematical foundation of the boost operator approach for the fermion model. In fact, we obtain some higher conserved quantities of the fermion model using the boost operator.

hep-th↗