The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the one-dimensional (1D) t-J model is assessed by comparison with the same quantities in the 1D t- ${\mathrm{J}}_{\mathrm{z}}$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At ${\mathrm{J}}_{\mathrm{z}}$ /t= ${0}^{+}$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. At the transition point, the t- ${\mathrm{J}}_{\mathrm{z}}$ ground state has zero (static) charge correlations and very short-ranged (static) spin correlations, whereas the t-J ground state is critical. The t- ${\mathrm{J}}_{\mathrm{z}}$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the t-J model. A major transformation of the t-J spin excitations takes place between two distinct regimes within the Luttinger-liquid phase, while the t- ${\mathrm{J}}_{\mathrm{z}}$ spin excitations are found to change much more gradually. In the t- ${\mathrm{J}}_{\mathrm{z}}$ model, phase separation is accompanied by N\'eel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the t-J model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by two-spinon excitations) in the phase-separated state.The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the one-dimensional (1D) t-J model is assessed by comparison with the same quantities in the 1D t-${\mathrm{J}}_{\mathrm{z}}$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At ${\mathrm{J}}_{\mathrm{z}}$/t=${0}^{+}$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. At the transition point, the t-${\mathrm{J}}_{\mathrm{z}}$ ground state has zero (static) charge correlations and very short-ranged (static) spin correlations, whereas the t-J ground state is critical. The t-${\mathrm{J}}_{\mathrm{z}}$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the t-J model. A major transformation of the t-J spin excitations takes place between two distinct regimes within the Luttinger-liquid phase, while the t-${\mathrm{J}}_{\mathrm{z}}$ spin excitations are found to change much more gradually. In the t-${\mathrm{J}}_{\mathrm{z}}$ model, phase separation is accompanied by N\'eel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the t-J model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by two-spinon excitations) in the phase-separated state.

arXiv:cond-mat/9609101Physical review. B, Condensed matterMar 1, 199718 citations

The one-dimensional XXZ model with long-range interactions

Lindberg Lima Gonçalves, André P. Vieira, Lucas Pinheiro Coutinho

arXiv:cond-mat/0008230Journal of Magnetism and Magnetic MaterialsMay 1, 20011 citation

Critical dynamics of long-range models on dynamical Lévy lattices

Riccardo Aiudi, Raffaella Burioni, A. Vezzani

We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimensions in the presence of long-range interactions, ${J}_{ij}\ensuremath{\propto}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$. We implement a local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\ensuremath{\sigma}$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long-range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\ensuremath{\sigma}$, highlighting that the onset of the short-range regime for the dynamical critical properties appears to occur at a value of $\ensuremath{\sigma}$ which differs from the equilibrium one.We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimensions in the presence of long-range interactions, ${J}_{ij}\ensuremath{\propto}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$. We implement a local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\ensuremath{\sigma}$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long-range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\ensuremath{\sigma}$, highlighting that the onset of the short-range regime for the dynamical critical properties appears to occur at a value of $\ensuremath{\sigma}$ which differs from the equilibrium one.

arXiv:2303.18057Physical review. B./Physical review. BJun 28, 20233 citations

Dynamical conditions in a simple soluble model

Cornel Eftimiu

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fieldsOct 1, 19661 citation

Dissipative quantum disordered models

Leticia F. Cugliandolo

This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.

Jan 1, 20063 citations

Critical indices for models with long-range interaction

Mukadas Dmukhtasibovich Missarov

Theoretical and Mathematical PhysicsFeb 1, 19813 citations

{\mathrm{J}}_{\mathrm{z}}

model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At

{\mathrm{J}}_{\mathrm{z}}

/t=

{0}^{+}

we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. At the transition point, the t-

{\mathrm{J}}_{\mathrm{z}}

ground state has zero (static) charge correlations and very short-ranged (static) spin correlations, whereas the t-J ground state is critical. The t-

{\mathrm{J}}_{\mathrm{z}}

charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the t-J model. A major transformation of the t-J spin excitations takes place between two distinct regimes within the Luttinger-liquid phase, while the t-

{\mathrm{J}}_{\mathrm{z}}

spin excitations are found to change much more gradually. In the t-

{\mathrm{J}}_{\mathrm{z}}

model, phase separation is accompanied by N\'eel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the t-J model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by two-spinon excitations) in the phase-separated state.

z

as a function of the decay parameter $\ensuremath{\sigma}$, highlighting that the onset of the short-range regime for the dynamical critical properties appears to occur at a value of $\ensuremath{\sigma}$ which differs from the equilibrium one.