Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum phase transition (QPT). In this paper, we illustrate that the system dynamics can be elucidated by considering the precession of a collection of free-pseudo spins under a magnetic field based on the exact results of extended Kitaev chains. The topology of the driven Hamiltonian is determined by the average winding number of the nonequilibrium state. Furthermore, we establish that the singularity of the DQPT arises from two perpendicular pseudo-spin vectors associated with the pre- and post-quenched Hamiltonians. Moreover, we investigate the distinct behaviors of the dynamic pairing order parameter in both topological and non-topological regions. These findings offer valuable insights into the non-equilibrium behavior of topological superconductors, contributing to the understanding of the resilience of topological properties in driven quantum systems.
Kitaev's model of spins interacting on a honeycomb lattice describes a quantum spin-liquid, where an emergent static $\mathbb{Z}_2$ gauge field is coupled to Majorana fermions. In the presence of an external magnetic field and for a range of interaction strengths, the system behaves as a gapped, non-Abelian quantum spin-liquid. In this phase, the vortex excitations of the emergent $\mathbb{Z}_2$ gauge field have Majorana zero modes bound to them. Motivated by recent experimental progress in measuring and characterizing real materials that could exhibit spin-liquid behavior, we analytically cal…
We report on magnetization $M(H)$, dc/ac magnetic susceptibility $χ(T)$, specific heat $C_{\mathrm{m}}(T)$ and muon spin relaxation ($μ$SR) measurements of the Kitaev honeycomb iridate Cu$_2$IrO$_2$ with quenched disorder. In spite of the chemical disorders, we find no indication of spin glass down to 260~mK from the $C_{\mathrm{m}}(T)$ and $μ$SR data. Furthermore, a persistent spin dynamics observed by the zero-field muon spin relaxation evidences an absence of static magnetism. The remarkable observation is a scaling relation of $χ[H,T]$ and $M[H,T]$ in $H/T$ with the scaling exponent $α=0.2…
Arizona State University（亚利桑那州立大学）；Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS)（俾路支信息技术、工程与管理科学大学）；University of Toronto（多伦多大学）；Canadian Institute for Advanced Research（加拿大高级研究院）
We study low-energy properties of spin-$S$ Kitaev models in an anisotropic limit. The effective form of a local conserved quantity is derived in the low-energy subspace. We find this is the same as that of $S=1/2$ case for the half-integer spins but shows a different form for the integer spins. Applying the perturbation theory to the anisotropic Kitaev model, we obtain the effective Hamiltonian. In the integer spin case, the effective model is equivalent to a free spin model under an uniform magnetic field, where quantum fluctuations are quenched. On the other hand, in the half-integer case, t…
Kinetic obstruction to pairing in the doped Kitaev-Heisenberg ladder
University of Missouri（密苏里大学）；University of Tennessee（田纳西大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Quantum Science Center（量子科学中心）；Materials Science and Engineering Institute, University of Missouri（密苏里大学材料科学与工程研究所）
Elementary excitations in highly entangled states such as quantum spin liquids may exhibit exotic statistics, different from those obeyed by fundamental bosons and fermions. Excitations called non-Abelian anyons are predicted to exist in a Kitaev spin liquid - the ground state of an exactly solvable model proposed by Kitaev almost a decade ago. A smoking-gun signature of such non-Abelian anyons, namely a half-integer quantized thermal Hall conductivity, was recently reported in $α$-RuCl$_3$. While fascinating, a microscopic theory for this phenomenon in $α$-RuCl$_3$ remains elusive because the…
An attempt is made to quantum simulate the topological classification, such as winding number, geometric phase and symmetry properties for a quantum simulated Kitaev chain. We find, α (ratio between the spin-orbit coupling and magnetic field) and the range of momentum space of consideration, which plays a crucial role for the topological classification. We show explicitly that the topological quantum phase transition does not occurs at k = 0 limit for the quantum simulated Kitaev chain. We observe that the quasi-particle mass of the Majorana mode plays the significant role in topological quant…
The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Is…
Kitaev quantum spin liquids have been the focus of intense research effort thanks to the discovery of various materials (e.g., RuCl3) that approximate their intriguing physics. In this paper we construct a mean-field approximation for a moir`e superlattice emerging in twisted Kitaev bilayers in terms of solutions of commensurate bilayers. We show that the band structure of deconfined spinons, defined on the mini-Brillouin zone of the superlattice, is greatly modified. The system exhibits a hyper-magic manifold: a series of nearly perfectly-flat bands appear at energies above the lowest gap, ex…
We explore the dynamics of long-range Kitaev chain by varying pairing interaction exponent, $α$. It is well known that distinctive characteristics on the nonequilibrium dynamics of a closed quantum system are closely related to the equilibrium phase transitions. Specifically, the return probability of the system to its initial state (Loschmidt echo), in the finite size system, is expected to exhibit very nice periodicity after a sudden quench to a quantum critical point. Where the periodicity of the revivals scales inversely with the maximum of the group velocity. We show that, contrary to exp…
The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as $α$-RuCl$_3$. Currently, two competing scenarios exist for the intermediate field phase of this compound ($B=7-10$ T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian natu…
Anyonic excitations emerging from a Kitaev spin liquid can form a basis for quantum computers. Searching for such excitations motivated intense research on the honeycomb iridate materials. However, access to a spin liquid ground state has been hindered by magnetic ordering. Cu2IrO3 is a new honeycomb iridate without thermodynamic signatures of a long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of Cu2IrO3. We find a two-component depolarization with slow and fast relaxation rates corresponding to distinct regions with dynamic and static magnetism, respect…
We investigate the magnetic excitations of the hyperhoneycomb Kitaev magnet $β$-$\text{Li}_2\text{IrO}_3$ by means of inelastic Raman scattering. The spectra exhibits a coexistence of a broad scattering continuum and two sharp low-energy peaks at 2.5 meV and 3 meV, with a distinctive polarization dependence. While the continuum is suggestive of fractional quasi-particles emerging from a proximate quantum spin liquid phase, the sharp peaks provide the first experimental signature of the `non-Loudon-Fleury' one-magnon scattering processes proposed recently [Phys. Rev. B 104, 144412 (2021)]. The …
We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in the phase diagram of the considered systems are thereby promoted to topologically robust non-Hermitian (NH) nodal phases emerging in the coherent long-time evolution of a dynamically equilibrating system. In the framework of non-equilibrium Green's function methods within the conserving second Born approximation, we predict observable signatures of these nov…
We theoretically investigate Majorana zero modes emerging in an anisotropic XY spin chain with second neighbor interactions. The spin chain is mathematically equivalent to the Kitaev chain composing of spinless fermions if only nearest-neighbor interactions are considered. Recent studies on the Kitaev chain with long-ranged interactions, have presented coexistence of several Majorana zero modes. Investigating the topological phase diagram of the anisotropic XY spin chain with second neighbor interactions, we find coexistence of several Majorana zero modes similar to the Kitaev chain. However, …
We develop a general framework for studying the equilibrium and non-equilibrium properties of arbitrary networks of Sachdev-Ye-Kitaev clusters coupled to thermal baths. We proceed to apply this technique to the problem of energy transport, which is known to be diffusive due to the strange metal behavior of these models. We use the external baths to impose a temperature gradient in the system and study the emerging non-equilibrium steady state using the Schwinger-Keldysh formalism. We consider two different configurations for the baths, implementing either a boundary or bulk driving, and show t…
In the pseudospin-$\frac{1}{2}$ honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions, named Kitaev ($K$) and $Γ$, leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the $Γ$ model remains controversial. In particular, the phase diagram of the $KΓ$ model with ferromagnetic $K$ and antiferromagnetic $Γ$ interactions has been intensively studied because of its relevance to candidate materials such as $α$-RuCl$_{3}$. Numerical studies…
We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ (where spin symmetry is enlarged to SU$(M)$) study of the normal state to superconductor phase transition. We describe the transition temperature, the sup…
We study the response to sudden local perturbations of highly excited Quantum Ising Spin Chains. The key quantity encoding this response is the overlap between time-dependent wave functions, which we write as a two-times Loschmidt echo. Its asymptotics at long time differences contains crucial information about the structure of the highly excited non-equilibrium environment induced by the quench. We compute the Echo perturbatively for a weak local quench but for arbitrarily large global quench, using a cumulant expansion. Our perturbative results suggest that the Echo decays exponentially, rat…
We propose a $d-$dimensional interacting Majorana fermion model with quenched disorder, which gives us a continuous quantum phase transition between a diffusive thermal metal phase with a finite entropy density to an insulator phase with zero entropy density. This model is based on coupled Sachdev-Ye-Kitaev model clusters, and hence has a controlled large-$N$ limit. The metal-insulator transition is accompanied by a spontaneous time-reversal symmetry breaking. We perform controlled calculations to show that the diffusion constant jumps to zero discontinuously at the metal-insulator transition,…
The nematic electronic state and its associated nematic critical fluctuations have emerged as potential candidates for superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with other magnetically-ordered phases poses significant challenges in establishing their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe$_{0.89}$S$_{0.11}$, we provide a unique access to a clean nematic quantum phase transition in the absence of a long-range magnetic order. We find that in the proximity of the nematic phase transiti…
Layered α-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this exotic state has been reported under a modest in-plane magnetic field, such behavior is largely inconsistent with theoretical expectations of Kitaev phases emerging only in out-of-plane fields. These predicted field-induced states have been mostly out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunneling spectroscopy, magnetotransport, electron diffraction, and ab initio calculat…
Disorder-induced quantum Fisher information in topological quantum systems
BITS Pilani KK Birla Goa Campus（比拉戈亚校园）；Harish-Chandra Research Institute（哈里什-昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Università di Trento（特伦托大学）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究所-基础物理与应用特伦托研究所）
We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via current-current interactions. The model is shown to have a lattice realization in an array of two-leg quantum spin-1/2 ladders. We study the model both in the presence and absence of time-reversal symmetry, within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes wh…
Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical quantum phase transitions [DQPTs], are a recently introduced attempt to classify the myriad of possible phenomena which can occur in far from equilibrium closed quantum systems. In this work, we analytically investigate the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$ fermionic superfluids. We find that the presence of non-analyticities in the echo is not invariant under global rotations of the superfluid phase. We remedy this deficiency by introducing a more general notion of a grand canonical…
Topology, symmetry, electron correlations, and the interplay between them have formed the cornerstone of our understanding of quantum materials in recent years and are used to identify new emerging phases. While the first two give a fair understanding of noninteracting and, in many cases, weakly interacting wave function of electron systems, the inclusion of strong correlations could change the picture substantially. The Kondo lattice model is a paradigmatic example of the interplay of electron correlations and conduction electrons of a metallic system, describing heavy fermion materials and a…
The emerging and screening of local magnetic moments in solids has been investigated for more than 60 years. Local vacancies as in graphene or in Heavy Fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for sy…
