arXiv subjects

Masaaki Nakamura

Publications and source records attributed to Masaaki Nakamura.

53 records · Page 3Linked to original sources

arXiv2005

Ground-state phase diagram of the one-dimensional Hubbard-model with an alternating potential

We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential--a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and a band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidences to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.

cond-mat.str-el↗

arXiv2005

Exact Plaquette-Ordered Ground States in the Generalized Hubbard Model in Arbitrary Dimensions

We show the existance of the exact plaquette-ordered ground states of the Hubbard model including site-off-diagonal interactions in arbitrary dimensions, by decomposing the Hamiltonian as sum of products of projection operators for each spin sector. The obtatined exact ground states are interpreted as Néel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagomé lattice, and determine parameter regions of the exact ground states.

cond-mat.str-el↗

arXiv2004

Quarter-filled extended Hubbard model with alternating transfer integral: Two-dimensional Ising transition in the ground state

We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine-Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of $4k_{\rm F}$ density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances to the charge-ordered phase observed in the charge-transfer organic salts.

cond-mat.str-el↗

arXiv2003

Scalar chiral ground states of spin ladders with four-spin exchanges

We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a $Z_2 \times Z_2 \times Z_2$ symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.

cond-mat.str-el↗

arXiv2002

Identification of topologically different valence bond states in spin ladders

We discuss relation between three different methods to identify topologically distinct short-range valence-bond ground states in spin-$\frac12$ two-leg ladders: the string order parameters, the level-crossing method, and the ground-state expectation value of the twist operator. For this purpose we reexamine a phase transition in the frustrated spin ladder. We propose a proper bosonization of the string order parameters. Then, these three methods are shown to be equivalent reflecting the $Z_2\times Z_2$ symmetry breaking of the order and the disorder fields of the two-dimensional Ising model.

cond-mat.stat-mech↗

arXiv2002

Ground state of antiferromagnetic Heisenberg two-leg ladder in terms of the valence-bond solid picture

We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder.

cond-mat.str-el↗

arXiv2002

Novel Order Parameter to Characterize Valence-Bond-Solid States

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the configuration of the valence bonds. This allows us to determine the phase transition point in between different VBS states accurately. We demonstrate this theory in the bond-alternating Heisenberg chain and in the frustrated spin ladder.

cond-mat.stat-mech↗

arXiv2001

Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method.

cond-mat.stat-mech↗

arXiv2001

Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. We identify $z_L$ with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian model. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing approach.

cond-mat.str-el↗

arXiv2001

Exact Bond-Located Spin Ground State in the Hubbard Chain with Off-Diagonal Coulomb Interactions

We show the existence of an exact ground state in certain parameter regimes of one-dimensional half-filled extended Hubbard model with site-off-diagonal interactions. In this ground state, the bond-located spin correlation exhibits a long-range order. In the case when the spin space is SU(2) symmetric, this ground state degenerates with higher spin states including a fully ferromagnetic state. We also discuss the relation between the exact bond-ordered ground state and the critical bond-spin-density-wave phase.

cond-mat.str-el↗

arXiv2000

Tricritical Behavior in the Extended Hubbard Chains

Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction $V$) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the U(1) $\otimes$ SU(2) symmetry of the electron system. Near the $U=2V$ line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-$V$ region involving spin-gap and BKT-type metal-insulator transitions.

cond-mat.str-el↗

arXiv2000

Role of Bond-Bond Interaction in the Extended Hubbard Chain

Phase diagrams of the one-dimensional extended Hubbard model with a nearest neighbor interaction $V$ and site-off-diagonal (bond-charge $X$ and bond-bond $W$) interactions at half-filling are obtained numerically, using the level-crossing approach for finite-size clusters. This analysis is straightforward extension of the preceding work [cond-mat/9909277], where only the $X$ term is considered as a site-off-diagonal term. Similarly to the $X$ term, the $W$ term enlarges bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for $W<0$ and $W>0$ cases, respectively. In the strong-coupling region, however, the $W$ term causes ferromagnetism for $W>0$, and shifts the boundary of the phase separation in the $U/t\ll-1$ region, which are different from the roles of the $X$ term. In addition, we discuss a parameter region where the BSDW state is the exact ground state, and show that the exactly solvable point appears just on the phase boundary between the BSDW and the ferromagnetic phases.

cond-mat.str-el↗

arXiv1999

Spin-Gap Phases in Tomonaga-Luttinger Liquids

We give the details of the analysis for critical properties of spin-gap phases in one-dimensional lattice electron models. In the Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is shown to be equivalent to that of the level-crossing of the singlet and the triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the t-J model, and the t-J-J' model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.

cond-mat.str-el↗

arXiv1999

Mechanism of CDW-SDW Transition in One Dimension

The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by the Gaussian and the spin-gap transitions under charge-spin separation, or by a direct CDW-SDW transition. We determine these phase boundaries by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and the spin-gap transitions take place separately from weak- to intermediate-coupling region. This means that the third phase exists between the CDW and the SDW states. Our results are also consistent with those of the strong-coupling perturbative expansion and of the direct evaluation of order parameters.

cond-mat.str-el↗

arXiv1998

Spin-Gap Phase in the One-Dimensional t-J-J' Model

The spin-gap phase of the one-dimensional t-J-J' model is studied by the level-crossing of the singlet and the triplet excitation spectra. The phase boundary obtained between the Tomonaga-Luttinger and the spin-gap phases is remarkably consistent with the analytical results at the $J,J'\to 0$ and the low-density limits discussed by Ogata et al. The spin-gap phase has a single domain in the phase diagram even if the spin gap opens at half-filling. The phase boundary coincides with the $K_ρ=1$ line where the Tomonaga-Luttinger liquid behaves as free electrons, in the low-density region. The relation between our method and the solution of the two-electron problem is also discussed.

cond-mat.str-el↗

arXiv1997

Renormalization group analysis of the spin-gap phase in the one-dimensional t-J model

We study the spin-gap phase in the one-dimensional t-J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also check that the universality class of the transition belongs to the $k=1$ SU(2) Wess-Zumino-Witten model.

cond-mat.str-el↗

arXiv1997

Phase separation as an instability of the Tomonaga-Luttinger liquid

Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional $t$-$J$ model, to study the universal property of the $c=1$ conformal field theory with U(1) symmetry near the $K\to\infty$ instability. On the analogy of the spinless fermion, we discuss that the compressibility behaves as $κ\propto (J_c-J)^{-1}$, and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite size effect from the result of the exact diagonalization.

cond-mat.str-el↗