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Results in Physics

Characterization of gapless topological quantum phase transition via magnetocaloric effect

Linjie Ding, Yimeng Sun, Y. Zhong

Published Mar 12, 2024• 2 citations
Publisher

Abstract

It has attracted much attention on the interplay between topology and criticality in topological quantum systems, i.e., gapless topological quantum phase transition (TQPT) on critical lines. It is demonstrated that the magnetocaloric effect (MCE) is able to signal the gapless TQPT in an extended Kitaev chain, which is witnessed by the unusual critical behavior of joint effect of Grüneison ration (GR) and isothermal entropy change. We uncover the conventional TQPT between gapped phases showing high symmetry (HS) and non-HS critical points with self-duality, which is signaled by the finite value of GR as T→0 and the largest inverse MCE with T-linear relation of isothermal entropy change. Two critical lines intersect at a multicritical point, at which there is a T-1 critical divergence of GR as well as T1/2 critical behavior of isothermal entropy change. It manifests a “weak” gapless TQPT on the one critical line, demonstrated by the shifting zero-crossing of GR without the largest inverse MCE. On the other critical line, it shows a “strong” gapless TQPT, which is evidenced by the negative dip of GR together with the largest inverse MCE. Our work provides a novel thermodynamic perspective on gapless TQPT.

DOI
10.1016/j.rinp.2024.107572

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It has attracted much attention on the interplay between topology and criticality in topological quantum systems, i.e., gapless topological quantum phase transition (TQPT) on critical lines. It is demonstrated that the magnetocaloric effect (MCE) is able to signal the gapless TQPT in an extended Kitaev chain, which is witnessed by the unusual critical behavior of joint effect of Grüneison ration (GR) and isothermal entropy change. We uncover the conventional TQPT between gapped phases showing high symmetry (HS) and non-HS critical points with self-duality, which is signaled by the finite value of GR as T→0 and the largest inverse MCE with T-linear relation of isothermal entropy change. Two critical lines intersect at a multicritical point, at which there is a T-1 critical divergence of GR as well as T1/2 critical behavior of isothermal entropy change. It manifests a “weak” gapless TQPT on the one critical line, demonstrated by the shifting zero-crossing of GR without the largest inverse MCE. On the other critical line, it shows a “strong” gapless TQPT, which is evidenced by the negative dip of GR together with the largest inverse MCE. Our work provides a novel thermodynamic perspective on gapless TQPT.
We investigate the quantum phase transition(QPT) and magnetocaloric effect(MCE) of a tetrameric chain with three-spin interaction using Green’s function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic field and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Gru¨neisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic(de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Gru¨neisen ratio can testify various quantum phases explicitly.
We investigate the quantum phase transition (QPT) and magnetocaloric effect (MCE) of a tetrameric chain with three-spin interaction using Green's function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic held and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Grüneisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic (de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Grüneisen ratio can testify various quantum phases explicitly.
Abstract The quantum phase transition (QPT) and quantum criticality of an anisotropic spin-1/2 XY chain under the interplay of magnetic field and Dzyaloshinskii–Moriya (DM) interaction, which is interpreted as an electric field, are investigated, wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order. It is shown that the thermal Drude weight is a good quantity to characterize the gapped ( D th = 0) and gapless ( D th > 0) ground states. The continuous QPT is marked by a quantum critical point (QCP) associated with entropy accumulation, which is manifested by a characteristic Güneisen ratio (GR) with or without self-duality symmetry. It is shown that at a self-dual QCP, the GR keeps a finite value as T → 0, while at a general QCP without self-duality symmetry, it displays a power-law temperature dependent divergence: Γ( T , r c ) ∼± T −1 , which provides a novel thermodynamic means for probing QPT.
Recently topological states of matter have witnessed a new physical phenomenon where both edge modes and gapless bulk coexist at topological quantum criticality. The presence and absence of edge modes on a critical line can lead to an unusual class of topological phase transition between the topological and nontopological critical phases. We explore the existence of this new class of topological phase transitions in a generic model representing the topological insulators and superconductors and we show that such transition occurs at a multicritical point, i.e., at the intersection of two critical lines. To characterize these transitions we reconstruct the theoretical frameworks, which include bound state solution of the Dirac equation, winding number, correlation factors, and scaling theory of the curvature function to work for the criticality. Critical exponents and scaling laws are discussed to distinguish between the multicritical points, which separate the critical phases. Entanglement entropy and its scaling in the real space provide further insights into the unique transition at criticality revealing the interplay between fixed point and critical point at the multicriticalities.
The phase transition between gapped topological phases represents a class of unconventional criticality beyond the Landau paradigm. However, recent research has shifted attention to topological phases without a bulk gap, where the phase transitions between them are still elusive. In this work, based on large-scale density-matrix renormalization-group techniques, we investigate the critical behaviors of the extended quantum XXZXXZXXZ model obtained by the Kennedy-Tasaki transformation. Using fidelity susceptibility as a diagnostic, we obtain a complete phase diagram, which includes both topological nontrivial and trivial gapless phases. Furthermore, as the XXZXXZXXZ-type anisotropy parameter $\mathrm{\ensuremath{\Delta}}$ varies, both the critical points hc{h}_{c}hc​ and correlation length exponent $\ensuremath{\nu}$ remain the same as in the $\mathrm{\ensuremath{\Delta}}=0$ case, characterized by c=3/2c=3/2c=3/2 (Ising plus free boson) conformal field theory. Our results indicate that fidelity susceptibility can effectively detect and reveal a stable unconventional critical line between the topologically distinct gapless phases for general $\mathrm{\ensuremath{\Delta}}$. This work serves as a valuable reference for further research on phase transitions within the gapless topological phase of matter.
The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.