Quantum criticality of bosonic systems with the Lifshitz dispersion

Abstract

We study the quantum criticality of the Lifshitz ϕ 4 -theory below the upper critical dimension. Two fixed points, one Gaussian and the other non-Gaussian, are identified with zero and finite interaction strengths, respectively. At zero temperature the particle density exhibits different powerlaw dependences on the chemical potential in the weak and strong interaction regions. At finite temperatures, critical behaviors in the quantum disordered region are mainly controlled by the chemical potential. In contrast, in the quantum critical region critical scalings are determined by temperature. The scaling ansatz remains valid in the strong interaction limit for the chemical potential, correlation length, and particle density, while it breaks down in the weak interaction one. As approaching the upper critical dimension, physical quantities develop logarithmic dependence on dimensionality in the strong interaction region. These results are applied to spin-orbit coupled bosonic systems, leading to predictions testable by future experiments. Introduction.-Quantum phase transitions, uniquely driven by quantum fluctuations, appear when the ground state energy encounters non-analyticity via tuning a nonthermal parameter. Physical properties around quantum critical points (QCPs) are of extensive interests because the interplay between quantum and thermal critical fluctuations strongly influence the dynamical and thermodynamic quantities, giving rise to rich quantum critical properties beyond the classical picture [1,2]. Quantum critical fluctuations are believed to be responsible for various emergent phenomena, including the non-Fermi liquid behaviors in heavy fermion systems, unconventional superconductivity, and novel spin dynamics in onedimensional quantum magnets [3][4][5][6].

Magnetization-governed magnetoresistance anisotropy in the topological semimetal CeBi

“…The uniqueness of the observed magnetoresistance anisotropy in CeBi at TN/2 < T < TN is further corroborated in its topologically trivial counterpart CeSb [57,58]. Similar to CeBi which is in the ground state Type IA at low temperatures (T < TN/2), CeSb also has a transition to its ground state Type IA at T » 8 K (~ TN/3) upon cooling in zero field [50].…”

Ground-state properties of dilute Bose systems with synthetic dispersion laws

“…Here in the problem of the ground-state properties of interacting BR bosons (2) we find a similar fermionization effect: there exists a non-trivial fixed point of the RG transformation which in the dilute limit is responsible for a quadratic dependence of the chemical potential on the particle density (µ ∝ n 2 ) as found in a one-dimensional free Fermi gas. The same conclusion using the same technique was recently reached in the context of the bosons obeying the quartic dispersion law (4) [24]. RG method has been also employed to study the low-energy physics of spinless bosons with BR dispersion law (1) in two dimensions [25]; a related three-dimensional problem has been considered in Ref.…”

Achieving continuously tunable critical exponents for long-range spin systems simulated with trapped ions

“…Based on the general dimensional analysis, we can express the magnon density as a function of dimensionless coupling constantg(Λ) andμ(Λ) via n = Λ d f (g,μ). Here Λ is the momentum cutoff, f is a scaling function,g(Λ) = g 2 (Λ)Λ − ,μ(Λ) = µ(Λ)Λ −φ , and = φ − d. The scaling behaviors ofg(b) andμ(b) under scale transformation Λ → Λe b can be obtained via RG equations, a general approach to critical phenomena [34][35][36][37]. Following the standard calculations, we derive the following RG equations…”