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arXiv:2209.10390 · Physical Review Research

From Kosterlitz-Thouless to Pokrovsky-Talapov transitions in spinless fermions and spin chains with next-nearest-neighbor interactions

Natalia Chepiga

Published Dec 30, 2022• 6 citations
arXivHTMLPDF

Abstract

We investigate the nature of the quantum phase transition out of density-wave phase in a spinless fermion model with nearest- and next-nearest-neighbor interaction at one-third filling. Using extensive density matrix renormalization group (DMRG) simulations, we show that the transition changes it nature. For weak next-nearest-neighbor coupling the transition is of Kosterlitz-Thouless type, in agreement with bosonisation predictions. For large next-nearest-neighbor repulsion we provide numerical evidences that the transition belongs to the Pokrovsky-Talapov univerality class describing a nonconformal commensurate-incommensurate transition. We argue that the change of the nature of the transition is a result of incommensurability induced by frustration and realized even at zero doping. The implications in the context of the $XXZ$ chain with next-nearest-neighbor Ising interaction is briefly discussed.

DOI
10.1103/physrevresearch.4.043225

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We investigate the nature of the quantum phase transition out of density-wave phase in a spinless fermion model with nearest- and next-nearest-neighbor interaction at one-third filling. Using extensive density matrix renormalization group (DMRG) simulations, we show that the transition changes it nature. For weak next-nearest-neighbor coupling the transition is of Kosterlitz-Thouless type, in agreement with bosonisation predictions. For large next-nearest-neighbor repulsion we provide numerical evidences that the transition belongs to the Pokrovsky-Talapov univerality class describing a nonconformal commensurate-incommensurate transition. We argue that the change of the nature of the transition is a result of incommensurability induced by frustration and realized even at zero doping. The implications in the context of the XXZXXZXXZ chain with next-nearest-neighbor Ising interaction is briefly discussed.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.
We investigate the zero magnetization and ground state phase diagram of a spin-1/2 chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in the strongly interacting regime. Using density matrix renormalization group (DMRG) simulations, we discover two successive commensurate-incommensurate transitions of the nonconformal Pokrovsky-Talapov universality class, occurring even at zero magnetic field. We argue that the first transition marks the proliferation of solitonic discommensurations (kink-antikink pairs) in a critical phase with central charge c=2, emerging from a period-4 gapped phase. At the second transition, an incommensurate quadrupolar (or nematic) Luttinger liquid forms out of a gapped phase separation, via the condensation of two-magnon bound pairs. In the strongly interacting limit, the location of the two Pokrovsky-Talapov transitions can be analytically predicted with degenerate perturbation theory. Our results demonstrate that frustration alone is sufficient to drive continuous commensurate-incommensurate transitions of Mott type and stabilize complex objects with incommensurate quasi-long-range order without doping.
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions.Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations.The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles.In relation with recent studies, we show several emergent transition lines with a central charge c = 3/2 between the Luttinger liquid and the cluster Luttinger liquid phases.These results could be experimentally investigated using highly tunable quantum simulators.
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The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation predicts the occurrence of a floating incommensurate (IC) Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium relaxation (NER) simulations. In this paper, we first examine previously published results of both methods, and then investigate a higher transition temperature Tc1{T}_{c1}Tc1​ between the IC and paramagnetic phases. In the usual equilibrium simulation, we calculate the chain magnetization on larger lattices (up to $512\ifmmode\times\else\texttimes\fi{}512$ sites) and estimate ${T}_{c1}\ensuremath{\approx}1.16J$ with frustration ratio $\ensuremath{\kappa}(\ensuremath{\equiv}\ensuremath{-}{J}_{2}/{J}_{1})=0.6$. We examine the nature of the phase transition in terms of the Binder ratio gL{g}_{L}gL​ of spin overlap functions and the correlation-length ratio $\ensuremath{\xi}/L$. In the NER simulation, we observe the spin dynamics in equilibrium states by means of an autocorrelation function and also observe the chain magnetization relaxations from the ground and disordered states. These quantities exhibit an algebraic decay at $T\ensuremath{\lesssim}1.17J$. We conclude that the two-dimensional ANNNI model actually admits an IC phase transition of the KT type.
We study the interacting Kitaev chain with nearest-neighbor interactions and finite chemical potential using a combination of bosonization and density-matrix renormalization-group calculations. Focusing away from special exactly solvable lattice limits, we develop a continuum field-theoretic description of the generic finite-density interacting regime, where doping nonperturbatively modifies the competition between superconducting pairing and commensurate charge ordering. We show that the phase diagram consists of an intermediate incommensurate Luttinger liquid between the topological superconducting and commensurate charge-density-wave Mott phases, as well as a trivial band-insulating regime at large chemical potential. The commensurate--incommensurate and incommensurate--topological-superconducting phase boundaries are governed by Pokrovsky--Talapov and Berezinskii--Kosterlitz--Thouless criticality, respectively. We analyze the interacting topological superconducting regime and its boundary excitations. At the semiclassical level, and explicitly in the free-fermion boundary theory, the topological phase supports exponentially localized Majorana edge modes at interfaces between topological and trivial regions. We also construct a dual continuum fermionic representation in which this topological bulk sector is described instead by conventional symmetry breaking. This gives a continuum version of the SPT--SSB correspondence between different fermionic representations. Overall, our results provide an analytical description of one-dimensional interacting topological superconductors, from the competition between topology and commensurability and the resulting quantum criticality to the dual symmetry-breaking description of the topological phase.