Anisotropic long-range spin systems

Defenu, Nicoló; Trombettoni, Andrea; Ruffo, Stefano

doi:10.1103/physrevb.94.224411

Cited by 45 publications

(50 citation statements)

References 57 publications

(151 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2. Note that the equilibrium phase diagram of the long-range Kitaev chain radically differs from the one of the long-range quantum Ising model [37,38].…”

Section: Figmentioning

confidence: 98%

Universal dynamical scaling of long-range topological superconductors

et al. 2019

Self Cite

View full text Add to dashboard Cite

We study the out-of-equilibrium dynamics of p-wave superconducting quantum wires with longrange interactions, when the chemical potential is linearly ramped across the topological phase transition. We show that the heat produced after the quench scales with the quench rate δ according to the scaling law δ θ , where the exponent θ depends on the power law exponent of the longrange interactions. We identify the parameter regimes where this scaling can be cast in terms of the universal equilibrium critical exponents and can thus be understood within the Kibble-Zurek framework. When the electron hopping decays more slowly in space than pairing, it dominates the equilibrium scaling. Surprisingly, in this regime the dynamical critical behaviour arises only from paring and, thus, exhibits anomalous dynamical universality unrelated to equilibrium scaling. The discrepancy from the expected Kibble-Zurek scenario can be traced back to the presence of multiple universal terms in the equilibrium scaling functions of long-range interacting systems close to a second order critical point.

show abstract

“…2. Note that the equilibrium phase diagram of the long-range Kitaev chain radically differs from the one of the long-range quantum Ising model [37,38].…”

Section: Figmentioning

confidence: 98%

Universal dynamical scaling of long-range topological superconductors

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this work, we deal with the previous issues by first considering the case of classical O(N ) models in dimension d ≥ 2 for weak LR interactions, see Sections II-III. The goal of these sections is to review the FRG treatment for classical models and to set up the ground for the study of the quantum case, which is the subject of Sections IV-IV C. Our presentation is based on the formalism developed and the results obtained in [27][28][29], while the presentation follows the one in [30]. Our main objectives is to present such findings in an unified and compact way, providing as well details on the derivations and new results on the topic of weak LR spin systems.…”

mentioning

confidence: 99%

Criticality of spin systems with weak long-range interactions

Defenu¹,

Codello²,

Ruffo³

et al. 2020

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical O(N ) spin models and we then move to quantum spin systems. I. INTRODUCTIONIn this Special Issue several aspects of the equilibrium and dynamical properties of systems with long-range (LR) interactions are discussed. In the paper we apply concepts and tools developed for LR systems, including the modern renormalization group approach, to the study of spin models with weak LR interactions. Such interactions are able to modify the universal properties of the systems in which they act, but anyway preserve the extensivity of the thermodynamic quantities. Our main goal is to present and apply the formalism of the functional renormalization group (FRG) to weak LR systems and show the capability of the FRG to clarify their critical properties, which are in many cases still unknown and sometimes diffucult to obtain with other approaches.Given the wide framework already presented in the other contributions to this Special Issue, it is not necessary to extensively emphasize that LR interactions play an important and paradigmatic role in the study of many body interacting systems, such as O(N ) symmetric models. Indeed, the importance of LR interactions is motivated by their presence in several systems ranging from plasma physics to astrophysics and cosmology [1,2].In order to understand the typical phenomena occurring in spin models with power-law LR couplings and define the weak LR regime, let us first consider the classical O(N ) symmetric models, whose Hamiltonian reads(1)The spin variables S i are unit vectors with N components, placed at the sites, labeled by the index i, of a d dimensional lattice. The coupling constant J is constant for a decay exponent σ > 0, conversely for σ ≤ 0 the coupling constant J needs to be rescaled by an appropriate power of the system size to absorb the divergence of the interaction energy density the thermodynamic limit [1,2]. When σ > 0 the model may have a second order phase transition. The main result is that three different regimes can occur as a function of the parameter σ [3, 4]:• for σ ≤ d/2 the mean-field approximation correctly describes the universal behavior;• for σ greater than a threshold value, σ * , the model has the same critical...

show abstract

“…2.2, the series of data m H /∆ terminate around σ ≈ 1.6 (D ≈ 2.25). Such a feature is supported by the analytic formula (12) in the sense that for large σ (large ǫ), the Higgs particle becomes obscure nonetheless. We make a brief overview for the fixed-D = 3(= 2 + 1)-lattice analyses.…”

Section: Comparison With the Preceding Results Via The σ ↔ D Relationmentioning

confidence: 85%

Criticality of the Higgs mass for the long-range quantum XY chain: Amplitude ratio between the Higgs and paramagnetic gaps

Nishiyama

2019

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

The quantum XY spin chain with the interactions decaying as a power law 1/r 1+σ of the distance between spins r was investigated with the exact diagonalization method. Here, the constituent spin is set to S = 1, which enables us to incorporate the biquadratic interactions so as to realize the order-disorder transition with the O(2) symmetry maintained. Thereby, in the ordered phase, we resolved the Higgs mass m H out of the Goldstoneexcitation continuum by specifying Higgs-particle's quantum numbers to adequate indices. We then turn to the analysis of the critical amplitude ratio m H /∆ (∆: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio m H /∆ gets enhanced gradually in agreement with the ǫ(= 4 − D)-expansion-renormalization-group result; here, we resort to the σ ↔ D relation advocated recently in order to establish a relationship between the renormalization-group result and ours.

show abstract

Anisotropic long-range spin systems

Cited by 45 publications

References 57 publications

Universal dynamical scaling of long-range topological superconductors

Universal dynamical scaling of long-range topological superconductors

Criticality of spin systems with weak long-range interactions

Criticality of the Higgs mass for the long-range quantum XY chain: Amplitude ratio between the Higgs and paramagnetic gaps

Contact Info

Product

Resources

About