Topological Quantum Phase Transition Research Articles

Chirality reversal quantum phase transition in flat-band topological insulators.

Quantum anomalous Hall effect generates dissipationless chiral conductive edge states in materials with large spin-orbit coupling and strong, intrinsic, or proximity magnetization. The topological indexes of the energy bands are robust to smooth variations in the relevant parameters. Topological quantum phase transitions between states with different Chern numbers require the closing of the bulk bandgap: C=1→C=1/2 corresponds to the transition from a topological insulator to gapless in k=0 state- quantum anomalous semimetal. Within the Bernevig-Hughes-Zhang model of 2D topological quantum well, this study identifies another type of topological phase transition induced by a magnetic field. The transition C=±1→C=∓1occurs when the monotonic Zeeman field reaches the threshold value and thus triggers the reversal of edge modes chirality. The calculated threshold depends on the width of the conduction and valence bands and is more experimentally achievable the flatter the bands. The effect of the topological phase transition ∆C=2 can be observed experimentally as a jump in magnetoresistance.&#xD.

Robust Teleportation of a Surface Code and Cascade of Topological Quantum Phase Transitions

Teleportation is a facet where quantum measurements can act as a powerful resource in quantum physics, as local measurements allow us to steer quantum information in a nonlocal way. While this has long been established for a single Bell pair, the teleportation of a many-qubit entangled state using nonmaximally entangled resources presents a fundamentally different challenge. Here, we investigate a tangible protocol for teleporting a long-range entangled surface-code state using elementary Bell measurements and its stability in the presence of coherent errors that weaken the Bell entanglement. We relate the underlying threshold problem to the physics of anyon condensation under weak measurements and map it to a variant of the Ashkin-Teller model of statistical mechanics with Nishimori-type disorder, which gives rise to a cascade of phase transitions. Tuning the angle of the local Bell measurements, we find a continuously varying threshold. Notably, the threshold moves to infinity for the X+Z angle along the self-dual line—indicating that infinitesimally weak entanglement is sufficient in teleporting a self-dual topological surface code. Our teleportation protocol, which can be readily implemented in dynamically configurable Rydberg-atom arrays, thereby gives guidance for a practical demonstration of the power of quantum measurements. Published by the American Physical Society 2024

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids.

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

Topological Transition in Aromatic and Quinonoid π-Conjugated Polymers Induced by Static Strain.

A topological quantum phase transition has been identified for the first time for 24 π-conjugated polymers as a function of external longitudinal strain due to a level crossing of the frontier orbitals at the topological phase transition. Topological phase is determined by the presence/absence of edge states. Out of the 24 polymers 15 are traditionally assigned an aromatic character, and 9 are traditionally assigned a quinonoid character. We find that all aromatic ones correspond to the trivial topological phase (Zak invariant, Z2 = 0), while all of the quinonoid ones to the nontrivial topological phase (Z2 = 1) replacing the intuitive characterization of aromatic/quinonoid with the physically well-defined Zak invariant. Unique topological phase transition as a function of tensile strain can be achieved for four of the quinonoid ones. Tensile strain in these cases leads to a reduction of the bandgap. We introduced a figure of merit for indicating the efficiency of achievable very small bandgap upon the application of external strain.

Topology and curvature effects in the photonics of ring – split ring – cuboid transitions

Topological transitions in various materials are actively being studied, including topological quantum phase transitions, going beyond the Landau theory and the concept of the order parameter. Here we propose the concept of a transition between two structures with different topology using the example of the transition between a flat dielectric ring and a split ring and its further unbending into a rectangular Fabry-Pérot resonator. Experimentally and theoretically, we discovered the lifting of the degeneracy of the CW-CCW photonic modes of the ring and the formation of two families: topological, which acquire an additional phase π, equal to the Berry phase in a thin Möbius strip, and ordinary ones, which do not acquire an additional phase. Topological modes arise due to the gradual “cutting” of one antinode of the field by a gap into two antinodes as the angular size of the gap increases from zero to one degree. Thus, using a topological Fabry-Pérot resonator with variable curvature and fixed length, resonant modes with an arbitrary non-integer number of waves are realized and a new generation of resonators is created with the prospect of unique classical and quantum applications.

Dynamical topological quantum phase transitions in high-order topological systems

Dynamical topological quantum phase transitions in high-order topological systems

Disorder-induced topological quantum phase transitions in multigap Euler semimetals

We study the effect of disorder in systems having a nontrivial Euler class. As these recently proposed multigap topological phases come about by braiding non-Abelian charged band nodes residing between different bands to induce stable pairs within isolated band subspaces, novel properties may be expected. Namely, a modified stability and critical phases under the unbraiding to metals can arise when the disorder preserves the underlying C2T or PT symmetry on average. Employing elaborate numerical computations, we verify the robustness of associated topology by evaluating the changes in the average densities of states and conductivities for different types of disorders. Upon performing a scaling analysis around the corresponding quantum critical points, we retrieve a universality for the localization length exponent of ν=1.4±0.1 for Euler-protected phases, relating to two-dimensional percolation models. We generically find that quenched disorder drives Euler semimetals into critical metallic phases. Finally, we show that magnetic disorder can also induce topological transitions to quantum anomalous Hall plaquettes with local Chern numbers determined by the initial value of the Euler invariant. Published by the American Physical Society 2024

Error-tolerant parity detector of cat-state qubits based on a topological quantum phase transition

Error-tolerant parity detector of cat-state qubits based on a topological quantum phase transition

Robust discriminator of chiral molecules via a topological invariant.

We propose a scheme for chirality discrimination via a topological invariant. The physical model is based on a three-level subspace of a molecule. By modulating the components of the control field with proper frequencies, two different two-level effective Hamiltonians are derived for the left-handed and the right-handed molecules. We parameterize the effective Hamiltonians with two angles and demonstrate that a topological quantum phase transition can be induced by tuning the effective Rabi frequency if the molecule is right-handed. This phenomenon provides a method to discriminate the chirality of the molecule by measuring a topological invariant, i.e., the Chern number, of the parametric manifold. Since the Chern number is robust against perturbations to the system, the scheme is insensitive to the systematic errors of the control fields, the deviations of the modulation frequencies, and decoherence of the molecule. Therefore, the scheme may provide useful perspectives to construct a robust discriminator of chiral molecules.

Quantum oscillations and electronic features in V1− δ Sb2 single crystals

Nonsymmorphic compounds have attracted much interest owing to their potential nontrivial electronic states. Here, we grew V1−δSb2 single crystal with a nonsymmorphic space group I4/mcm and studied their de Haas–van Alphen oscillations. Orientation-dependent magnetization showed quantum oscillations, allowing determination of the three-dimensional Fermi surface and Berry phase. Our theoretical calculation implied that VSb2's band structures manifest flat bands along the Γ–X path, Dirac band crossings near the P and N points, and in the Γ–Z direction, and nontrivial surface states along the Γ¯–Z¯ line. However, the inconsistencies in observed and calculated quantum oscillation frequencies suggest that VSb2's band structures cannot nicely account for these electronic properties of our samples. This study reveals the profound impact of V vacancies on VSb2's electronic states, implying the possible topological quantum phase transition via defect engineering.

Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields

Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields

Detecting Quantum Topologic Phase Transitions Through The C-Function

Topological Quantum Field Theory or TQFT is a quantum field theory that calculates topological invariance in measurement theory and mathematical physics. In recent years, several attempts have been made to find efficient observations to determine the TQFT of quasiparticle properties. In this paper, we propose a different and very effective way to detect the critical points of TQFT by considering the system functions. We suggest the C-Function as a novel probe that is accurate for detecting the location of critical points on topological quantum. The C-function uses a holographic model to show a topological quantum phase transition between a simple topological isolation phase and a gapless Weyl semimetal. The quantum tipping point displays a strong Lifshitz-like anisotropy in the spatial direction, and a quantum phase transition that does not follow the standard Landau paradigm. The C-function precisely shows the global features of quantum criticality and distinguishes very accurately between two separate zero-temperature phases. Considering the C-function relationship with entanglement entropy can detect quantum phase transitions and can be applied outside the holographic framework.
 Keywords: quantum topologic, phase transitions, c-function

Characterization of gapless topological quantum phase transition via magnetocaloric effect

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 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.

Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein Condensation in Two Dimensions: Crossovers and Topological Quantum Phase Transitions

We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

Electric-field control of magnetic anisotropies: Applications to Kitaev spin liquids and topological spin textures

Magnetic anisotropies often originate from the spin-orbit coupling and determine magnetic ordering patterns. We develop a microscopic theory for dc electric-field controls of magnetic anisotropies in magnetic Mott insulators and discuss its applications to Kitaev materials and topological spin textures. Throughout this paper, we take a microscopic approach based on Hubbard-type lattice models, tight-binding models with onsite interactions. We derive a low-energy spin Hamiltonian from a fourth-order perturbation expansion of the Hubbard-type model. We show in the presence of a strong intra-atomic spin-orbit coupling that dc electric fields add non-Kitaev interactions such as a Dzyaloshinskii-Moriya interaction and an off-diagonal Γ′ interaction to the Kitaev-Heisenberg model and can induce a topological quantum phase transition between Majorana Chern insulating phases. We also investigate the interatomic Rashba spin-orbit coupling and its effects on topological spin textures. dc electric fields turn out to create and annihilate magnetic skyrmions, hedgehogs, and chiral solitons. We propose several methods of creating topological spin textures with external electromagnetic fields. Our theory clarifies that the strong but feasible electric field can control Kitaev spin liquids and topological spin textures. Published by the American Physical Society 2024

Strain-driven topological quantum phase transition in (pseudo)cubic (mixed)-Cs/MA/FA halide perovskites

First-order topological phase transition in noncentrosymmetric FAPbI3.

Bloch oscillations probed quantum phases in HgTe quantum wells

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x- and y-components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime.

Pressure-Induced Superconductivity and Topological Quantum Phase Transitions in the Topological Semimetal ZrTe2.

Topological transition metal dichalcogenides (TMDCs) have attracted much attention due to their potential applications in spintronics and quantum computations. In this work, the structural and electronic properties of topological TMDCs candidate ZrTe2 are systematically investigated under high pressure. A pressure-induced Lifshitz transition is evidenced by the change of charge carrier type as well as the Fermi surface. Superconductivity is observed at around 8.3GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum Tc of 5.6K for ZrTe2 . Furthermore, the theoretical calculations suggest the presence of multiple pressure-induced topological quantum phase transitions, which coexists with emergence of superconductivity. The results demonstrate that ZrTe2 with nontrivial topology of electronic states displays new ground states upon compression.

Quantum phase transition in CeCoIn5: Experimental facts and theory

The condensed-matter community is involved in a hot debate on the nature of quantum critical points (QCP) governing the low-temperature properties of heavy fermion metals. The smeared jump-like behavior revealed both in the residual resistivity and the Hall resistivity R H , along with the violation of the time invariance symmetry and the charge invariance , include the violation of quasiparticle-hole symmetry, and provide vital clues on the origin of both the non-Fermi-liquid behavior and QCP. For the first time, based on a number of important experimental data, we show that these experimental observations point out unambiguously that QCP of is accompanied by the symmetry violation, and QCP itself is represented by the topological fermion-condensation quantum phase transition (FCQPT) connecting two Fermi surfaces of different topological charges.

Steered Quantum Coherence as a Signature of Topological Quantum Phase Transitions in the Extended XY Model

AbstractIn recent years, there has been a surge of interest in exploring coherence measures and correlation measures to characterize topological quantum phase transitions (TQPTs). Here, motivated by the continued push in this direction, the steered quantum coherence (SQC) in the extended XY model is studied to analyze its capability in characterizing TQPTs. It is shown that the first derivative of SQC succeeds in signaling different critical points of TQPTs. In particular, it is found that the SQC is a long‐range correlation and the first derivative of SQC can always accurately identify TQPTs for different site distance.