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

arXiv:cond-mat/0504027 · Physical Review B

Doped two-leg ladder with ring exchange: Exact diagonalization and density matrix renormalization group computations

Guillaume Roux, Steven R. White, Sylvain Capponi, Andreas Martin Läuchli, Didier Poilblanc

Published Jul 14, 2005• 14 citations
arXivHTMLPDF

Abstract

The effect of a ring exchange on doped two-leg ladders is investigated combining exact diagonalization (ED) and density matrix renormalization group (DMRG) computations. We focus on the nature and weights of the low-energy magnetic excitations and on superconducting pairing. The stability with respect to this cyclic term of a remarkable resonant mode originating from a hole pair-magnon bound state is examined. We also find that, near the zero-doping critical point separating rung-singlet and dimerized phases, doping reopens a spin gap.

DOI
10.1103/physrevb.72.014523

Related papers

Spin-charge separation in two-leg t-J ladders

Luhang Yang, Elbio R. Dagotto

Spin-charge separation is a hallmark of one-dimensional fermionic systems, yet its realization in higher dimensions remains an open question. To address this issue, we investigate a two-leg t-J ladder using the density matrix renormalization group (DMRG) method and its time-dependent extension. By analyzing ground-state correlations and single-particle removal spectra, we systematically examine the effects of plaquette diagonal hopping, spin exchange, and hole doping. Within appropriate parameter regimes, these factors drive the system from the well-known Luther Emery phase, with gapped spin and gapless charge modes, into a Luttinger liquid phase characterized by gapless spin and charge excitations, where signatures of spin-charge separation emerge. In combination with previous studies using exact diagonalization, our results provide evidence that spin-charge separation may persist in wider ladder systems.

arXiv:2605.09705•May 10, 2026•0 citations

Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases

Guillaume Roux, E. Orignac, Steven R. White +1 more

We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit ($t\text{\ensuremath{-}}J$ model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust, but immediately acquires algebraic transverse (i.e., along rungs) current correlations which are commensurate with the $4{k}_{F}$ density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio $J∕t$: we found strong anomalies at low $J∕t$ only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and $1∕2$. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a $4{k}_{F}$ charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.

arXiv:0707.3017•Physical Review B•Nov 2, 2007•51 citations

Thermodynamics of the t−J Ladder: A Stable Finite-Temperature Density Matrix Renormalization Group Calculation

Beat Ammon, Matthias Troyer, Thomas Maurice Rice +1 more

Accurate numerical simulations of a doped $t\ensuremath{-}J$ model on a two-leg ladder are presented for the particle number, chemical potential, magnetic susceptibility, and entropy in the limit of large exchange coupling on the rung using a finite-temperature density matrix renormalization group method. This required an improved algorithm to achieve numerical stability down to low temperatures. The thermal dissociation of hole pairs and of the rung singlets are separately observed, and the evolution of the hole pair binding energy and magnon spin gap with hole doping is determined.

arXiv:cond-mat/9812144•Physical Review Letters•May 10, 1999•22 citations

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results

Alberto Nocera, Yan Wang, N. D. Patel +4 more

We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.

arXiv:1803.08597•Physical review. B./Physical review. B•May 31, 2018•21 citations

A Density-Matrix Renormalization Group Study of Quantum Spin Models with Ring Exchange

Alexander H. L. Chan

In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.

•Jul 4, 2012•0 citations

Cyclic spin exchange in cuprate spin ladders

Tamara S. Nunner, Philipp Brune, Thilo Kopp +2 more

We investigate the influence of a cyclic spin exchange ${J}_{\mathrm{cyc}}$ on the one- and two-triplet excitations of an undoped two-leg $S=1/2$ ladder, using the density-matrix renormalization group (DMRG). The dispersion of the $S=0$ two-triplet bound state is dramatically reduced by ${J}_{\mathrm{cyc}}$ due to a repulsion between triplets on neighboring rungs. In $(\mathrm{La},\mathrm{Ca}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ a consistent description of both the spin gap and the $S$=0 bound state requires ${J}_{\mathrm{cyc}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}0.20--0.27$ and ${J/J}_{\ensuremath{\perp}}\ensuremath{\approx}1.25--1.35.$ With these coupling ratios the recently developed dynamical DMRG yields an excellent description of the entire $S=0$ excitation spectrum observed in the optical conductivity, including the continuum contribution.

arXiv:cond-mat/0203472•Physical review. B, Condensed matter•Nov 27, 2002•63 citations
The effect of a ring exchange on doped two-leg ladders is investigated combining exact diagonalization (ED) and density matrix renormalization group (DMRG) computations. We focus on the nature and weights of the low-energy magnetic excitations and on superconducting pairing. The stability with respect to this cyclic term of a remarkable resonant mode originating from a hole pair-magnon bound state is examined. We also find that, near the zero-doping critical point separating rung-singlet and dimerized phases, doping reopens a spin gap.
Spin-charge separation is a hallmark of one-dimensional fermionic systems, yet its realization in higher dimensions remains an open question. To address this issue, we investigate a two-leg t-J ladder using the density matrix renormalization group (DMRG) method and its time-dependent extension. By analyzing ground-state correlations and single-particle removal spectra, we systematically examine the effects of plaquette diagonal hopping, spin exchange, and hole doping. Within appropriate parameter regimes, these factors drive the system from the well-known Luther Emery phase, with gapped spin and gapless charge modes, into a Luttinger liquid phase characterized by gapless spin and charge excitations, where signatures of spin-charge separation emerge. In combination with previous studies using exact diagonalization, our results provide evidence that spin-charge separation may persist in wider ladder systems.
We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit ($t\text{\ensuremath{-}}J$ model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust, but immediately acquires algebraic transverse (i.e., along rungs) current correlations which are commensurate with the 4kF4{k}_{F}4kF​ density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio J∕tJ∕tJ∕t: we found strong anomalies at low J∕tJ∕tJ∕t only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and 1∕21∕21∕2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a 4kF4{k}_{F}4kF​ charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.
Accurate numerical simulations of a doped $t\ensuremath{-}J$ model on a two-leg ladder are presented for the particle number, chemical potential, magnetic susceptibility, and entropy in the limit of large exchange coupling on the rung using a finite-temperature density matrix renormalization group method. This required an improved algorithm to achieve numerical stability down to low temperatures. The thermal dissociation of hole pairs and of the rung singlets are separately observed, and the evolution of the hole pair binding energy and magnon spin gap with hole doping is determined.
We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard UUU values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.
In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.
We investigate the influence of a cyclic spin exchange Jcyc{J}_{\mathrm{cyc}}Jcyc​ on the one- and two-triplet excitations of an undoped two-leg S=1/2S=1/2S=1/2 ladder, using the density-matrix renormalization group (DMRG). The dispersion of the S=0S=0S=0 two-triplet bound state is dramatically reduced by Jcyc{J}_{\mathrm{cyc}}Jcyc​ due to a repulsion between triplets on neighboring rungs. In (La,Ca)14Cu24O41(\mathrm{La},\mathrm{Ca}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}(La,Ca)14​Cu24​O41​ a consistent description of both the spin gap and the SSS=0 bound state requires ${J}_{\mathrm{cyc}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}0.20--0.27$ and ${J/J}_{\ensuremath{\perp}}\ensuremath{\approx}1.25--1.35.$ With these coupling ratios the recently developed dynamical DMRG yields an excellent description of the entire S=0S=0S=0 excitation spectrum observed in the optical conductivity, including the continuum contribution.