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

Physical review. B, Condensed matter

Ground-state phase diagram of the one-dimensional extended Hubbard model: A density-matrix renormalization-group approach

G. P. Zhang

Published Oct 15, 1997• 45 citations
Publisher

Abstract

We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific $U,$ the critical value of ${V}_{c}$ for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As $U$ increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at ${U}_{c}=4--6,$ not ${U}_{c}=3$ as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length $N=4M$ than for chains of $N=4M+2,$ where $M$ is an integer, for the same $U$ and $V.$ The difference will diminish in the thermodynamic limit.

DOI
10.1103/physrevb.56.9189

Related papers

Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model

Eric Jeckelmann

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.

arXiv:cond-mat/0204244•Physical Review Letters•Nov 15, 2002•133 citations

Half-filled one-dimensional extended Hubbard model: Phase diagram and thermodynamics

S. Glocke, Andreas Klümper, Jesko Sirker

We study the thermodynamics of the one-dimensional extended Hubbard model at half filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be detected by measuring usual thermodynamic quantities such as the isothermal compressibility and the uniform magnetic susceptibility. For the isothermal compressibility, we show that universal crossing points exist, which allow us to accurately determine the line where the charge gap vanishes. By studying, in addition, several correlation functions, we confirm the existence of a phase with long-range dimer order (bond order), which has been a matter of debate for several years. According to our calculations, this phase is located in a narrow region between the spin-density and charge-density wave phases up to a tricritical point, which we estimate to be at ${U}_{t}=6.7\ifmmode\pm\else\textpm\fi{}0.2$, ${V}_{t}=3.5\ifmmode\pm\else\textpm\fi{}0.1$. Our results for the phase diagram are in good agreement with the most recent zero-temperature density-matrix renormalization group study; however, they disagree in some important aspects from the most recent Quantum-Monte-Carlo study.

arXiv:0707.1015•Physical Review B•Oct 24, 2007•50 citations

Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling

G. P. Zhang

It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio ${U/V}_{c}=2,$ where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.

Physical review. B, Condensed matter•Oct 2, 2003•28 citations

Phase Diagram of the One-Dimensional Half-Filled Extended Hubbard Model

Satoshi Ejima, Satoshi Nishimoto

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).

arXiv:0710.0673•Physical Review Letters•Nov 20, 2007•119 citations

Ground-state phase diagram of the one-dimensional extended Hubbard model

Joel W. Cannon, Richard T. Scalettar, Eduardo Fradkin

We study the ground-state phase diagram of the extended Hubbard model through the Lanczos method using charge-density-wave order-parameter distribution functions and finite-size scaling. We confirm the presence of a tricritical point, and estimate the phase boundary to occur at V=2.92\ifmmode\pm\else\textpm\fi{}0.04 at U=5.5, and at V=1.${65}_{\mathrm{\ensuremath{-}}0.05}^{+0.10}$ at U=3.0. We estimate the tricritical point to occur above U=3.5. Despite the restriction to small lattices, the increased accuracy of the Lanczos approach appears to provide a more precise estimate of the phase boundary and tricritical point than use of the Monte Carlo simulation.

Physical review. B, Condensed matter•Sep 15, 1991•71 citations

Quantum information analysis of the phase diagram of the half-filled extended Hubbard model

Cornelius Mund, Örs Legeza, R. M. Noack

We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.

arXiv:0904.4673•Physical Review B•Jun 25, 2009•37 citations
We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific U,U,U, the critical value of Vc{V}_{c}Vc​ for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As UUU increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at Uc=4−−6,{U}_{c}=4--6,Uc​=4−−6, not Uc=3{U}_{c}=3Uc​=3 as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length N=4MN=4MN=4M than for chains of N=4M+2,N=4M+2,N=4M+2, where MMM is an integer, for the same UUU and V.V.V. The difference will diminish in the thermodynamic limit.
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.
We study the thermodynamics of the one-dimensional extended Hubbard model at half filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be detected by measuring usual thermodynamic quantities such as the isothermal compressibility and the uniform magnetic susceptibility. For the isothermal compressibility, we show that universal crossing points exist, which allow us to accurately determine the line where the charge gap vanishes. By studying, in addition, several correlation functions, we confirm the existence of a phase with long-range dimer order (bond order), which has been a matter of debate for several years. According to our calculations, this phase is located in a narrow region between the spin-density and charge-density wave phases up to a tricritical point, which we estimate to be at ${U}_{t}=6.7\ifmmode\pm\else\textpm\fi{}0.2$, ${V}_{t}=3.5\ifmmode\pm\else\textpm\fi{}0.1$. Our results for the phase diagram are in good agreement with the most recent zero-temperature density-matrix renormalization group study; however, they disagree in some important aspects from the most recent Quantum-Monte-Carlo study.
It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio U/Vc=2,{U/V}_{c}=2,U/Vc​=2, where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.
We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).
We study the ground-state phase diagram of the extended Hubbard model through the Lanczos method using charge-density-wave order-parameter distribution functions and finite-size scaling. We confirm the presence of a tricritical point, and estimate the phase boundary to occur at V=2.92\ifmmode\pm\else\textpm\fi{}0.04 at U=5.5, and at V=1.${65}_{\mathrm{\ensuremath{-}}0.05}^{+0.10}$ at U=3.0. We estimate the tricritical point to occur above U=3.5. Despite the restriction to small lattices, the increased accuracy of the Lanczos approach appears to provide a more precise estimate of the phase boundary and tricritical point than use of the Monte Carlo simulation.
We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.