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/9702126 · Physical review. B, Condensed matter

Phase separation as an instability of the Tomonaga-Luttinger liquid

Masaaki Nakamura, K. Nomura

Published Nov 15, 1997• 9 citations
arXivHTMLPDF

Abstract

Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional $t\ensuremath{-}J$ model to study the universal property of the $c=1$ conformal field theory with U(1) symmetry near the $K\ensuremath{\rightarrow}\ensuremath{\infty}$ instability. By analogy to the spinless fermion, we argue that the compressibility behaves as $\ensuremath{\kappa}\ensuremath{\propto}{(J}_{c}\ensuremath{-}{J)}^{\ensuremath{-}1},$ 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.

DOI
10.1103/physrevb.56.12840

Related papers

Spin-gap phases in Tomonaga-Luttinger liquids

Masaaki Nakamura, Atsuhiro Kitazawa, K. Nomura

We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In 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 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 $t\ensuremath{-}J$ model, and the $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$ 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.

arXiv:cond-mat/9904381•Physical review. B, Condensed matter•Sep 15, 1999•22 citations

Emergent Carroll symmetry at phase separation in one-dimensional lattice systems

Sourav Biswas, Ashutosh Dubey, Saikat Mondal +3 more

Asymptotic behavior of generic Tomonaga-Luttinger liquid in the vicinity of phase-separated regions is known to produce an instability where well-known relativistic Conformal Field Theory (CFT) techniques fail. In this paper, we introduce an analytic paradigm that provides a continuum description of this important issue. We show that there is an emergent Carrollian symmetry when phase separation is reached, and techniques of Carroll CFT, as opposed to its relativistic relative, are central to the understanding of the physics. We work with the analogous spinless fermionic system in this region and capture the transition across this phase separation. Our numerical results corroborate the density-density correlations intrinsically computed using Carroll CFT. We further test the framework in a number of lattice systems, namely the spinless and spinfull fermionic models with distinct microscopic content, and find the same scaling at the transition. We discuss the scope of the framework and broader perspective.

arXiv:2501.16426•Physical review. B./Physical review. B•Jun 2, 2026•2 citations

Universal description of dissipative Tomonaga-Luttinger liquids with SU(N) spin symmetry: Exact spectrum and critical exponents

Kazuki Yamamoto, Norio Kawakami

Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with $\mathrm{SU}(N$) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with $\mathrm{SU}(N$) symmetry. We uncover that the spectrum of dissipative TL liquids with $\mathrm{SU}(N$) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of $c=1$ U(1) Gaussian CFT, and $N\ensuremath{-}1$ spin modes characterized by level-$1\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N$) Kac-Moody algebra with the conformal anomaly $c=N\ensuremath{-}1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the $\mathrm{SU}(N$) Calogero-Sutherland model with inverse-square long-range interactions.

arXiv:2207.04395•Physical review. B./Physical review. B•Jan 9, 2023•30 citations

Phase diagram of the one-dimensionalt-Jmodel

Masao Ogata, Marco U. Luchini, Sandro Sorella +1 more

The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around ${\mathit{J}}_{\mathit{c}}$/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.

Physical Review Letters•May 6, 1991•317 citations

Luttinger-liquid behavior and superconducting correlations int-Jladders

C A Hayward, Didier Poilblanc

The low-energy behavior of the isotropic t-J ladder system is investigated using exact diagonalization techniques, specifically finding the Drude weight, the charge velocity, and the compressibility. By applying the ideas of Luttinger-liquid theory, we determine the correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ which defines the behavior of the long-range correlations in the system. The boundary to phase separation is determined and a phase diagram is presented. At low electron density, a Tomonaga-Luttinger-like phase is stabilized while at higher electron densities a gapped phase with power law pairing correlations is stabilized: A large region of this gapped phase is found to exhibit dominant superconducting correlations. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9509123•Physical review. B, Condensed matter•May 1, 1996•81 citations

Phase separation in the Edwards model

Satoshi Ejima, Steffen Sykora, K. W. Becker +1 more

The nature of charge transport within a correlated background medium can be described by spinless fermions coupled to bosons in the model introduced by Edwards. Combining numerical density matrix renormalization group and analytical projector-based renormalization methods, we explore the ground-state phase diagram of the Edwards model in one dimension. Below a critical boson frequency, any long-range order disappears and the system becomes metallic. If the charge carriers are coupled to slow quantum bosons, the Tomonaga-Luttinger liquid is attractive and finally makes room for a phase separated state, just as in the $t$-$J$ model. The phase boundary separating the repulsive from the attractive Tomonaga-Luttinger liquid is determined from long-wavelength charge correlations, whereas fermion segregation is indicated by a vanishing inverse compressibility. On approaching phase separation, the photoemission spectra develop strong anomalies.

arXiv:1209.1810•Physical Review B•Oct 25, 2012•9 citations
Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model to study the universal property of the c=1c=1c=1 conformal field theory with U(1) symmetry near the K\ensuremath→\ensuremath∞K\ensuremath{\rightarrow}\ensuremath{\infty}K\ensuremath→\ensuremath∞ instability. By analogy to the spinless fermion, we argue that the compressibility behaves as \ensuremathκ\ensuremath∝(Jc\ensuremath−J)\ensuremath−1,\ensuremath{\kappa}\ensuremath{\propto}{(J}_{c}\ensuremath{-}{J)}^{\ensuremath{-}1},\ensuremathκ\ensuremath∝(Jc​\ensuremath−J)\ensuremath−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.
We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In 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 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 $t\ensuremath{-}J$ model, and the $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$ 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.
Asymptotic behavior of generic Tomonaga-Luttinger liquid in the vicinity of phase-separated regions is known to produce an instability where well-known relativistic Conformal Field Theory (CFT) techniques fail. In this paper, we introduce an analytic paradigm that provides a continuum description of this important issue. We show that there is an emergent Carrollian symmetry when phase separation is reached, and techniques of Carroll CFT, as opposed to its relativistic relative, are central to the understanding of the physics. We work with the analogous spinless fermionic system in this region and capture the transition across this phase separation. Our numerical results corroborate the density-density correlations intrinsically computed using Carroll CFT. We further test the framework in a number of lattice systems, namely the spinless and spinfull fermionic models with distinct microscopic content, and find the same scaling at the transition. We discuss the scope of the framework and broader perspective.
Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with SU(N\mathrm{SU}(NSU(N) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with SU(N\mathrm{SU}(NSU(N) symmetry. We uncover that the spectrum of dissipative TL liquids with SU(N\mathrm{SU}(NSU(N) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of c=1c=1c=1 U(1) Gaussian CFT, and $N\ensuremath{-}1$ spin modes characterized by level-1SU(N1\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N1SU(N) Kac-Moody algebra with the conformal anomaly $c=N\ensuremath{-}1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the SU(N\mathrm{SU}(NSU(N) Calogero-Sutherland model with inverse-square long-range interactions.
The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around Jc{\mathit{J}}_{\mathit{c}}Jc​/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.
The low-energy behavior of the isotropic t-J ladder system is investigated using exact diagonalization techniques, specifically finding the Drude weight, the charge velocity, and the compressibility. By applying the ideas of Luttinger-liquid theory, we determine the correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ which defines the behavior of the long-range correlations in the system. The boundary to phase separation is determined and a phase diagram is presented. At low electron density, a Tomonaga-Luttinger-like phase is stabilized while at higher electron densities a gapped phase with power law pairing correlations is stabilized: A large region of this gapped phase is found to exhibit dominant superconducting correlations. \textcopyright{} 1996 The American Physical Society.
The nature of charge transport within a correlated background medium can be described by spinless fermions coupled to bosons in the model introduced by Edwards. Combining numerical density matrix renormalization group and analytical projector-based renormalization methods, we explore the ground-state phase diagram of the Edwards model in one dimension. Below a critical boson frequency, any long-range order disappears and the system becomes metallic. If the charge carriers are coupled to slow quantum bosons, the Tomonaga-Luttinger liquid is attractive and finally makes room for a phase separated state, just as in the ttt-JJJ model. The phase boundary separating the repulsive from the attractive Tomonaga-Luttinger liquid is determined from long-wavelength charge correlations, whereas fermion segregation is indicated by a vanishing inverse compressibility. On approaching phase separation, the photoemission spectra develop strong anomalies.