Exact solution of a spin-12XXchain with three-site interactions in a random transverse field: Influence of randomness on the quantum phase transition

Abstract

We present exact results for the ground-state and thermodynamic properties of the spin-1/2 XX chain with three-site interactions in a random (Lorentzian) transverse field. We discuss the influence of randomness on the quantum critical behavior known to be present in the nonrandom model. We find that at zero temperature the characteristic features of the quantum phase transition, such as kinks in the magnetization versus field curve, are smeared out by randomness. However, at low but finite temperatures signatures of the quantum critical behavior are preserved if the randomness is not too large. Even the quantum critical region may be slightly enlarged for very weak randomness. In addition to the exact results for Lorentzian randomness we present a more general discussion of an arbitrarily random transverse magnetic field based on the inspection of the moments of the density of states.PACS numbers: 75.10.Jm Keywords: quantum phase transitions, random quantum spin chains, multi-site interactions, Green functions, density of states I. INTRODUCTORY REMARKSIn recent years the theory of quantum phase transitions has been in the focus of very active research. 1-3The quantum phase transitions take place at zero temperature by changing a control parameter and emerge as a result of competing different ground-state phases. Importantly, quantum phase transitions can influence the behavior of systems over a wide range of the phase diagram at nonzero (sometimes quite large) temperatures. Exactly solvable quantum models exhibiting a quantum phase transition are notoriously rare. A well-known example of a solvable model is the spin-1/2 Ising chain in a transverse field, where a zero-temperature transition from the ordered quantum Ising phase (small transverse fields) to the disordered quantum paramagnetic phase (large transverse fields) takes place. This model is often used for illustration of basic concepts in the quantum phase transition theory.2,4-8 In general, spin-1/2 XY chains 9 provide an excellent ground for various statistical mechanics studies since in many cases the calculations can be performed without any approximation. Moreover, there are some real-life compounds which can be viewed as realizations of one-dimensional spin-1/2 XY models. 10-13Quite recently, two other classes of solvable models have been found, namely a two-dimensional Kitaev model 14 and a spin-1/2 XY chain with multi-site interactions 15-17 (see also Ref. 18). The model belonging to the latter class is of interest in this paper. This model has an essentially richer ground-state phase diagram as the standard one-dimensional spin-1/2 XY model. In particular, it may exhibit several gapless spinliquid phases and quantum phase transitions between them. 16,17On the other hand, quantum models with random Hamiltonian parameters present another class of models for which an exact solution cannot be found easily. A solvable model with diagonal Lorentzian disorder was introduced by Lloyd.19 Later on Lloyd's idea was used to study random spin-1/2 XX chains.20...

Quantum phase transitions in a generalized compass chain with three-site interactions

“…We find that a finite gap separates occupied from empty bands except when h = h c , see Eq. (30). A small value of J * does not modify the critical field and the gap vanishes linearly for θ = π/2, see inset in Fig.…”

“…We remark that the number of gapless modes determine the effective central charge and the coefficients of the area-law violating term of bipartite entanglement entropy [52,53]. Notably, the chiral-II phase is a dedicated phase of the critical XX model with three-site XZY−YZX interactions added [29][30][31][32][33][34], while this phase is absent for anisotropic XY model [38]. Here we observe the three-site XZY−YZX interactions in the GCM surprisingly triggers both chiral states for arbitrary θ, and two different Tomonaga-Luttinger liquids reflect the importance of Fermi surface topology.…”

“…The form of P y 2 is the well-known XZX+YZY type of three-site interaction and remains solvable in the frame of Jordan-Wigner fermionization [29,30]. A little algebra will yield that three-site XZX+YZY interactions acts here as a renormalization (momentum-dependent) of the magnetic field h in the Hamiltonian Eq.…”

“…Recently three-site interactions received considerable attention in a bit diverse context [28][29][30][31][32][33][34][35][36][37][38][39][40][41]. They also occur in an effective spin model in a magnetic field obtained from a 1D plaquette orbital model by an exact transformation, with spin dimers that replace plaquettes.…”

Magnetocaloric effect in spin-1/2 XX chains with three-spin interactions

“…It can be modeled assuming that on-site fields or intersite interactions acquire random values. The considered quantum spin chains admit an exact analytical solution for thermodynamics in the case when the transverse magnetic field is a random variable with the Lorentzian probability distribution 34 . As a result, with such a model it is possible to discuss the MCE in the presence of randomness.…”