Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Molecular Crystals and Liquid Crystals

Intra- and Inter-Chain Excitations near a Quantum Phase Transition in Quasi-One-Dimensional Conductors

Kenji Yonemitsu

Published Jan 1, 2002• 2 citations
Publisher

Abstract

We study intra- and inter-chain excitation spectra near a quantum phase transition in a spinless fermion model on a two-leg ladder at half filling by the finite-temperature density-matrix renormalization-group method. Above a critical strength of intrachain nearest-neighbor repulsion, a gap appears, accompanied with a long-range order of density modulation in the checkerboard pattern at zero temperature. The intra chain excitation spectra do not change so much in the gapless phase below the critical strength, while the inter chain excitation spectra are considerably altered by the intra chain repulsion even in the gapless phase. Relevance to the optical conductivity in quasi-one-dimensional electron systems is suggested.

DOI
10.1080/10587250210787

Related papers

Collective excitations and confinement in the excitation spectra of the spinless fermion model on a ladder

Kenji Yonemitsu

Intrachain and interchain local charge-transfer excitation spectra and the single-particle density of states are calculated in the spinless fermion model on a ladder with varying intrachain nearest-neighbor repulsion and interchain transfer integral at and near half filling by using the finite-temperature density-matrix renormalization-group method. Collective excitations are found to govern the low-energy intrachain spectra, while only individual local excitations are present in the interchain spectra. For strong intrachain repulsion, the low-energy motion of fermions is confined within a chain. The interchain motion of fermions is not bandlike but incoherent. As a consequence, the low-energy intrachain spectra are sensitive at half filling to the interchain transfer integral that weakens the density-density correlation along the chains. Similarly, the low-energy intrachain spectra are sensitive near half filling to the chemical potential that reduces the effect of the umklapp process. Similarities are pointed out between these findings and the experimentally observed, optical conductivity spectra in the quasi-one-dimensional organic conductors $(\mathrm{TMTSF}{)}_{2}X.$

Physical review. B, Condensed matter•Jul 31, 2002•0 citations

Charge-Density-Wave Formation in the Doped Two-Leg Extended Hubbard Ladder

Masahisa Tsuchiizu, Yoshikazu Suzumura

We investigate electronic properties of the doped two-leg Hubbard ladder with both the onsite and the nearest-neighbor Coulomb repulsions, by using the the weak-coupling renormalization-group method. It is shown that, for strong nearest-neighbor repulsions, the charge-density-wave state coexisting with the p-density-wave state becomes dominant fluctuation where spins form intrachain singlets. By increasing doping rate, we have also shown that the effects of the nearest-neighbor repulsions are reduced and the system exhibits a quantum phase transition into the d-wave-like (or rung-singlet) superconducting state. We derive the effective fermion theory which describes the critical properties of the transition point with the gapless excitation of magnon. The phase diagram of the two-leg ladder compound, Sr_{14-x}Ca_xCu_{24}O_{41}, is discussed.

arXiv:cond-mat/0311534•Journal of the Physical Society of Japan•Apr 15, 2004•12 citations

Density Matrix Renormalization Group and Quantum Information applied to Quantum Critical Phenomena in One-Dimensional Systems

L. Tincani

We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.

•Nov 25, 2008•0 citations

Charge-order transition in the extended Hubbard model on a two-leg ladder

Matthias Vojta C, R. E. Hetzel, R. M. Noack

We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion $V$ using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and $U=8t,$ we find evidence for a continuous phase transition between a homogeneous state at small $V$ and a broken-symmetry state with ``checkerboard'' [wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$] charge order at large $V.$ This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of $U/t$ on the transition and estimate the position of the tricritical points.

arXiv:cond-mat/9906101•Physical review. B, Condensed matter•Sep 15, 1999•34 citations

Phase diagram of the quarter-filled extended Hubbard model on a two-leg ladder

Matthias Vojta C, A. Hübsch, R. M. Noack

We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion $V$ using the density matrix renormalization-group technique. The ground state is homogeneous at small $V,$ a ``checkerboard'' charge-ordered insulator at large $V$ and not too small on site Coulomb repulsion U, and is phase separated for moderate or large $V$ and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.

arXiv:cond-mat/0008068•Physical review. B, Condensed matter•Jan 8, 2001•51 citations

Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

Alberto Nocera, N. D. Patel, Jaime A. Fernandez-Baca +2 more

We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing $U/t$ converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of $U/t$ of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

arXiv:1608.07717•Physical review. B./Physical review. B•Nov 28, 2016•18 citations
We study intra- and inter-chain excitation spectra near a quantum phase transition in a spinless fermion model on a two-leg ladder at half filling by the finite-temperature density-matrix renormalization-group method. Above a critical strength of intrachain nearest-neighbor repulsion, a gap appears, accompanied with a long-range order of density modulation in the checkerboard pattern at zero temperature. The intra chain excitation spectra do not change so much in the gapless phase below the critical strength, while the inter chain excitation spectra are considerably altered by the intra chain repulsion even in the gapless phase. Relevance to the optical conductivity in quasi-one-dimensional electron systems is suggested.
Intrachain and interchain local charge-transfer excitation spectra and the single-particle density of states are calculated in the spinless fermion model on a ladder with varying intrachain nearest-neighbor repulsion and interchain transfer integral at and near half filling by using the finite-temperature density-matrix renormalization-group method. Collective excitations are found to govern the low-energy intrachain spectra, while only individual local excitations are present in the interchain spectra. For strong intrachain repulsion, the low-energy motion of fermions is confined within a chain. The interchain motion of fermions is not bandlike but incoherent. As a consequence, the low-energy intrachain spectra are sensitive at half filling to the interchain transfer integral that weakens the density-density correlation along the chains. Similarly, the low-energy intrachain spectra are sensitive near half filling to the chemical potential that reduces the effect of the umklapp process. Similarities are pointed out between these findings and the experimentally observed, optical conductivity spectra in the quasi-one-dimensional organic conductors (TMTSF)2X.(\mathrm{TMTSF}{)}_{2}X.(TMTSF)2​X.
We investigate electronic properties of the doped two-leg Hubbard ladder with both the onsite and the nearest-neighbor Coulomb repulsions, by using the the weak-coupling renormalization-group method. It is shown that, for strong nearest-neighbor repulsions, the charge-density-wave state coexisting with the p-density-wave state becomes dominant fluctuation where spins form intrachain singlets. By increasing doping rate, we have also shown that the effects of the nearest-neighbor repulsions are reduced and the system exhibits a quantum phase transition into the d-wave-like (or rung-singlet) superconducting state. We derive the effective fermion theory which describes the critical properties of the transition point with the gapless excitation of magnon. The phase diagram of the two-leg ladder compound, Sr_{14-x}Ca_xCu_{24}O_{41}, is discussed.
We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.
We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and U=8t,U=8t,U=8t, we find evidence for a continuous phase transition between a homogeneous state at small VVV and a broken-symmetry state with ``checkerboard'' [wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$] charge order at large V.V.V. This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of U/tU/tU/t on the transition and estimate the position of the tricritical points.
We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization-group technique. The ground state is homogeneous at small V,V,V, a ``checkerboard'' charge-ordered insulator at large VVV and not too small on site Coulomb repulsion U, and is phase separated for moderate or large VVV and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.