arXiv subjects

Xiong-Jun Liu

Publications and source records attributed to Xiong-Jun Liu.

At least 19 recordsLinked to original sources

arXiv2026

Observation of a tripartite quantum phase for coexisting extended, localized, and critical states

The disordered quantum world hosts three fundamental types of states: extended, localized, and critical, of which the critical states are confined to fine-tuned critical points or mobility edges in randomly disordered systems. The tripartite phase, with all three types of states coexisting over finite spectral windows, represents a hallmark distinction between quasiperiodic and truly random systems in the localization physics. Here, we report the realization of this exotic phase in a quasi-periodically driven orbital optical lattice with ultracold atoms. The optical lattice with a quasiperiodic Floquet modulation coupling s and p orbitals is realized in experiment and shown to host the tripartite phase from exact theory. We develop a two-stage protocol to precisely prepare and detect the three types of quantum states. The characteristic exponents of these states are determined from expansion dynamics, showing their distinct universal transport properties. Our study marks a significant advancement in exploring unconventional critical phenomena and localization physics with ultracold atoms.

cond-mat.quant-gas↗

arXiv2026

Experimental observation of exact quantum critical states

Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical, with the third one exhibiting the exotic properties in-between the former two. Confirming the presence of critical states is challenging, as it typically necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple superconducting qubit quantum system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges.

quant-ph↗

arXiv2026

Giant and robust Josephson diode effect in multiband topological nanowires

We theoretically predict the giant and robust Josephson diode effect in quasi-one-dimensional topological Majorana nanowires in the regime with multiple subbands, which is expected to be relevant for the real experiment. In the multiband regime, the Majorana bound states and conventional Andreev bound states can naturally coexist, and respectively contribute to the fractional and conventional parts in the Josephson effect, with the former/latter having 4$π$/2$π$-periodicity. We show that the interplay between the two types of bound modes can produce a robust and giant diode effect in the deep topological phase regime. Notably, we unveil a novel spin parity exchange mechanism, occurring only in the multiband regime, which leads to a robust high efficiency plateau of the giant diode effect. This effect is a nontrivial consequence of the balanced Fermi moment shifts of the multiple subbands in tuning the external magnetic field. Our finding highlights the subband engineering as a powerful tool to optimize the Josephson diode effect realistically and provides a new feasible signature to identify topological phase regime in superconducting nanowires.

cond-mat.mes-hall↗

arXiv2026

The fundamental localization phases in quasiperiodic systems: A unified framework and exact results

The disordered quantum systems host three classes of quantum states, the extended, localized, and critical, which bring up seven distinct fundamental phases in nature: three pure phases and four coexisting ones with mobility edges, yet a unified theory built on universal mechanism and full realization of all these phases has not been developed. Here we propose a unified framework based on a spinful quasiperiodic (QP) system which realizes all the fundamental localization phases, with the exact and universal results being obtained for their characterization. First, we show that the pure phases are obtained when the chiral(-like) symmetry preserves in the proposed spinful QP model, giving a criterion for emergence of the pure phases and otherwise the coexisting ones. Further, we uncover a novel mechanism for the critical states that their emergence is protected by the generalized incommensurate matrix element zeros in the spinful QP model, which considerably broadens rigorous realizations of the exotic critical states. We then show criteria of exact solvability for the present spinful QP system, with which we construct various exactly solvable models for all distinct localization phases. In particular, we propose two novel models, dubbed spin-selective QP lattice model and QP optical Raman lattice model, to achieve all basic types of mobility edges and all the seven fundamental phases of Anderson localization physics, respectively. The experimental scheme is proposed and studied in detail to realize these models with high feasibility. This study establishes a complete and profound theoretical framework which enables an in-depth exploration of the broad classes of all fundamental localization phenomena in QP systems, and offers key insights for constructing their exactly solvable models with experimental feasibility.

cond-mat.dis-nn↗

arXiv2026

Non-Abelian Statistics for Bosonic Symmetry-Protected Topological Phases

Symmetry-protected non-Abelian (SPNA) statistics opens new frontiers in quantum statistics and enriches the schemes for topological quantum computing. In this work, we propose a new paradigm of SPNA statistics in one-dimensional correlated bosonic symmetry-protected topological (SPT) phases and uncover exotic universal features from a systematic investigation. In particular, we show that for generic bosonic SPT phases described by real Hamiltonians, the SPNA statistics of topological zero modes fall into two distinct classes. The first class exhibits conventional braiding of hard-core bosonic zero modes. Furthermore, we discover a second class of unconventional braiding statistics characterized by a nonlinear transformation, featuring a fractionalization of the first class and reminiscent of the non-Abelian statistics of symmetry-protected Majorana pairs. The two distinct classes of statistics have topological origin in classifying non-Abelian Berry phases for braiding processes of real-Hamiltonian systems, distinguished by whether the holonomy involves a reflection operation. To illustrate, we focus on a specific bosonic SPT phase with particle-hole symmetry, and demonstrate that both classes of braiding statistics can be feasibly realized in a tri-junction with and without the aid of a controlled defect, respectively. Analytic and numerical results are given. We demonstrate how to encode logical qubits and implement both single- and two-qubit gates using the two classes of SPNA statistics. Finally, we propose feasible experimental schemes to observe these predictions and identify the parameter regimes for the high-fidelity braiding, paving the way for the experimental observation of our results in the near future.

cond-mat.str-el↗

arXiv2025

Non-interacting fractional topological Stark insulator

Fractional topological phases, such as the fractional quantum Hall state, usually rely on strong interactions to generate ground state degeneracy with gap protection and fractionalized topological response. Here, we propose a fractional topological phase without interaction in $(1+1)$-dimension, which is driven by the Stark localization on top of topological flat bands, different from the conventional mechanism of the strongly correlated fractional topological phases. A linear potential gradient applied to the flat bands drives the Stark localization, under which the Stark localized states may hybridize and leads to a new gap in the real space, dubbed the real space energy gap (RSEG). Unlike the integer topological band insulator obtained in the weak linear potential regime without closing the original bulk gap, the fractional topological Stark insulating phase is resulted from the RSEG when the linear potential gradient exceeds a critical value. We develop a theoretical formalism to characterize the fractional topological Stark insulator, and further show that the many-body state under topological pumping returns to the initial state only after multiple $2π$ periods of evolution, giving the fractional charge pumping, similar to that in fractional quantum Hall state. Finally, we propose how to realize the fractional topological Stark insulator in real experiment.

cond-mat.mes-hall↗

arXiv2025

Orbital Optical Raman Lattice

Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.

cond-mat.quant-gas↗

arXiv2025

Quantum many-body dynamics for fermionic t-J model simulated with atom arrays

The fermionic t-J model has been widely recognized as a canonical model for broad range of strongly correlated phases, particularly the high-Tc superconductor. Simulating this model with controllable quantum platforms offers new possibilities to probe high-Tc physics, yet suffering challenges. Here we propose a novel scheme to realize a highly-tunable extended t-J model in a programmable Rydberg-dressed tweezer array. Through engineering the Rydberg-dressed dipole-dipole interaction and inter-tweezer couplings, the fermionic t-J model with independently tunable exchange and hopping couplings is achieved. With the high tunability, we explore quantum many-body dynamics in the large J/t limit, a regime well beyond the conventional optical lattices and cuprates, and predict an unprecedented many-body self-pinning effect enforced by local quantum entanglement with emergent conserved quantities. The self-pinning effect leads to novel nonthermal quantum many-body dynamics, which violates eigenstate thermalization hypothesis in Krylov subspace. Our prediction opens a new horizon in exploring exotic quantum many-body physics with t-J model, and shall also make a step towards simulating the high-Tc physics in neutral atom systems.

cond-mat.quant-gas↗

arXiv2025

Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes

Majorana zero modes (MZMs) are the most intensively studied non-Abelian anyons. The Dirac fermion zero modes in topological insulators, which are symmetry-protected doubling of MZMs under fermion number conservation, offer an alternative approach to explore non-Abelian anyons. However, a unified model that elucidates the braiding statistics of these types of topological zero modes remains absent. We show that the minimal Kitaev chain model beyond fine-tuning regime provides a unified characterization of the non-Abelian statistics of both MZMs and Dirac fermion zero modes in different parameter regimes. In particular, we introduce a minimal tri-junction setting based on the minimal Kitaev chain model and show it facilitates the unified scheme of braiding Dirac fermion zero modes, as well as the MZMs in the assistance of a Dirac mode. This unified minimal model provides deeper insights into non-Abelian statistics, demonstrating that the non-Abelian braiding of MZMs can be continuously extended to encompass Dirac fermion zero modes. The minimal Kitaev chain has been realized in coupled quantum dots [Nature 614, 445 (2023)]. Our extension, which demonstrates novel nontrivial phases with non-Abelian MZM pairs and Dirac zero modes emerging in the broader parameter regimes without fine-tuning, expands the accessible experimental parameter space and enhances the feasibility of observing non-Abelian statistics in the minimal Kitaev chain model.

cond-mat.mes-hall↗

arXiv2025

Simulating non-Abelian statistics of parafermions with superconducting processor

Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we propose a novel experimental scheme for the quantum simulation of parafermions and their non-Abelian braiding statistics in superconducting (SC) circuits by realizing the $\mathbb{Z}_d$ plaquette model on a two-dimensional lattice. Two protocols using quantum circuits and non-destructive measurements are introduced to prepare the topologically ordered ground state, on which parafermion pairs are created by engineering dislocations. We then propose a generalized code deformation approach to realize the fusion and non-Abelian braiding of parafermions, and show the application of this approach to the $\mathbb{Z}_3$ parafermions. We also examine the real experimental parameter regime to confirm the feasibility of our scheme in SC devices. This work extends previous quantum simulations of topological defects in SC qubits to qudit systems and opens up a promising way for parafermion-based high-dimensional topological quantum computing with experimental feasibility.

quant-ph↗

arXiv2024

Anomalous universal quantum transport in 2D asymptotic quasiperiodic system

Quasiperiodic systems extend the concept of the Anderson transition to quasi-random and low-dimensional realms and have garnered widespread attention. Here, we propose the asymptotic quasiperiodic two-dimensional systems characterized by a sequence of rational magnetic fluxes, which have an irrational limit, and predict exotic universal wave-packet dynamics and transport phenomena associated with the asymptotic quasiperiodicity (AQP). The predictions unveil a class of multiple metal-insulator transitions driven by a novel interplay effect between AQP, relaxation, and finite temperature, which further reveals a unified and profound mechanism. Specifically, all the transport phenomena, including the wave-packet dynamics, the bulk and edge transport, are unified in the universal scaling laws unveiled in the asymptotic quasiperiodic regime, which demonstrate a nontrivial asymptotic connection to quantum phases in the quasiperiodic limit. Our work enriches the universal quantum transport phenomena, adds to the basic mechanisms underlying metal-insulator transitions, and opens up an avenue to study the exotic transport physics with AQP in high dimensions.

cond-mat.mes-hall↗

arXiv2024

Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas

The concept of non-Hermiticity has expanded the understanding of band topology leading to the emergence of counter-intuitive phenomena. One example is the non-Hermitian skin effect (NHSE), which involves the concentration of eigenstates at the boundary. However, despite the potential insights that can be gained from high-dimensional non-Hermitian quantum systems in areas like curved space, high-order topological phases, and black holes, the realization of this effect in high dimensions remains unexplored. Here, we create a two-dimensional (2D) non-Hermitian topological band for ultracold fermions in spin-orbit-coupled optical lattices with tunable dissipation, which exhibits the NHSE. We first experimentally demonstrate pronounced nonzero spectral winding numbers in the complex energy plane with non-zero dissipation, which establishes the existence of 2D skin effect. Further, we observe the real-space dynamical signature of NHSE in real space by monitoring the center of mass motion of atoms. Finally, we also demonstrate that a pair of exceptional points (EPs) are created in the momentum space, connected by an open-ended bulk Fermi arc, in contrast to closed loops found in Hermitian systems. The associated EPs emerge and shift with increasing dissipation, leading to the formation of the Fermi arc. Our work sets the stage for further investigation into simulating non-Hermitian physics in high dimensions and paves the way for understanding the interplay of quantum statistics with NHSE.

cond-mat.quant-gas↗

arXiv2024

Parafermions with symmetry-protected non-Abelian statistics

Non-Abelian anyons have garnered extensive attention for obeying exotic non-Abelian statistics and having potential applications to fault-tolerant quantum computing. While the prior research has predominantly focused on non-Abelian statistics without the necessity of symmetry protection, recent progresses have shown that symmetries can play essential roles and bring a notion of the symmetry-protected non-Abelian (SPNA) statistics. In this work, we extend the concept of SPNA statistics to strongly-correlated systems which host parafermion zero modes (PZMs). This study involves a few fundamental results proved here. First, we unveil a generic unitary symmetry mechanism that protects PZMs from local couplings. Then, with this symmetry protection, the PZMs can be categorized into two nontrivial sectors, each maintaining its own parity conservation, even though the whole system cannot be dismantled into separate subsystems due to nonlinear interactions. Finally, by leveraging the parity conservation of each sector and the general properties of the effective braiding Hamiltonian, we prove rigorously that the PZMs intrinsically obey SPNA statistics. To further confirm the results, we derive the braiding matrix at a tri-junction. We also propose a correlated quantum nanowire model that accommodates a pair of PZMs protected by mirror symmetry and satisfying the generic theory. This work shows a broad spectrum of strongly-correlated systems capable of hosting fractional SPNA quasiparticles and enriches our comprehension of fundamental quantum statistics linked to the symmetries that govern the exchange dynamics.

cond-mat.str-el↗

arXiv2024

Chiral spin liquid phase in an optical lattice at mean-field level

We study an optical Raman square lattice with $\mathrm{U}(1)$ synthetic gauge flux to show chiral spin liquid (CSL) phase for cold atoms based on slave-rotor theory and spinon mean-field theory, respectively. An effective U($1$) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find CSL phase at intermediate on-site Fermi Hubbard interacting regime. For the strong interacting regime we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that CSL phase is stabilized in the case of strong magnetic frustration. The two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.

cond-mat.str-el↗

arXiv2024

Surface Chern-Simons theory for third-order topological insulators and superconductors

Three-dimensional 3rd-order topological insulators (TOTIs) and superconductors (TOTSCs), as the highestorder topological phases hosting zero corner modes in physical dimension, has sparked extensive research interest. However, such topological states have not been discovered in reality due to the lack of experimental schemes of realization. Here, we propose a novel surface Chern-Simons (CS) theory for 3rd-order topological phases, and show that the theory enables a feasible and systematic design of TOTIs and TOTSCs. We show that the emergence of zero Dirac (Majorana) corner modes is entirely captured by an emergent $\mathbb{Z}_{2}$ CS term that can be further characterized by a novel two-particle Wess-Zumino (WZ) term uncovered here in the surfaces of three-dimensional topological materials. Importantly, our proposed CS term characterization and two-particle WZ term mechanism provide a unique perspective to design TOTIs (TOTSCs) in terms of minimal ingredients, feasibly guiding the search for underlying materials, with promising candidates being discussed. This work shall advance both the theoretical and experimental research for highest-order topological matters.

cond-mat.mes-hall↗

arXiv2024

Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms

Rydberg atom arrays offer promising platforms for quantum simulation of correlated quantum matter and raise great interests. This work proposes a novel stripe-lattice model with Raman superarray of Rydberg atoms to realize bosonic fractional quantum anomalous Hall (FQAH) phase. Two types of Rydberg states, arranged in a supperarray configuration and with Raman-assisted dipole-exchange couplings, are implemented to realize a minimal QAH model for hard-core bosons populated into a topological flat band with large bulk gap under proper tunable experimental condition. With this the bosonic FQAH phase can be further achieved and probed feasibly. In particular, a novel quench protocol is proposed to probe the fractionalized excitations by measuring the correlated quench dynamics featured by fractional charge tunneling between bulk and chiral edge modes in the open boundary.

cond-mat.quant-gas↗

arXiv2023

Realization and detection of Kitaev quantum spin liquid with Rydberg atoms

The Kitaev chiral spin liquid has captured widespread interest in recent decades because of its intrinsic non-Abelian excitations, yet the experimental realization is challenging. Here we propose to realize and detect Kitaev chiral spin liquid in a deformed honeycomb array of Rydberg atoms. Through a novel laser-assisted dipole-dipole interaction mechanism to generate both effective hopping and pairing terms for hard-core bosons, together with van der Waals interactions, we achieve the pure Kitaev model with high precision. The gapped non-Abelian spin liquid phase is then obtained by introducing Zeeman fields. Moreover, we propose innovative strategies to probe the chiral Majorana edge modes by light Bragg scattering and by imagining their chiral motion. Our work broadens the range of exotic quantum many-body phases that can be realized and detected in atomic systems, and makes an important step toward manipulating non-Abelian anyons.

cond-mat.str-el↗

arXiv2023

Anomalous second-order skin modes in Floquet non-Hermitian systems

The non-Hermitian skin effect under open boundary conditions is widely believed to originate from the intrinsic spectral topology under periodic boundary conditions. If the eigenspectra under periodic boundary conditions have no spectral windings (e.g., piecewise arcs) or a finite area on the complex plane, there will be no non-Hermitian skin effect with open boundaries. In this article, we demonstrate another scenario beyond this perception by introducing a two-dimensional periodically driven model. The effective Floquet Hamiltonian lacks intrinsic spectral topology and is proportional to the identity matrix (representing a single point on the complex plane) under periodic boundary conditions. Yet, the Floquet Hamiltonian exhibits a second-order skin effect that is robust against perturbations and disorder under open boundary conditions. We further reveal the dynamical origin of these second-order skin modes and illustrate that they are characterized by a dynamical topological invariant of the full time-evolution operator.

cond-mat.mes-hall↗