arXiv subjects

Sen Niu

Publications and source records attributed to Sen Niu.

15 recordsLinked to original sources

arXiv2026

Accessing Gapped Chiral Phase with Auxiliary-Assisted PEPS

It has been controversial whether infinite projected entangled pair state (PEPS) can faithfully describe chiral gapped phases in two dimensions or not. Finite-bond-dimension PEPS can capture many local and topological properties of chiral phases, but generically develop spurious long-range power-law like correlations. We introduce an auxiliary-assisted framework that bypass this obstruction by embedding the physical chiral system together with an auxiliary time-reversed partner, yielding a non-chiral enlarged representation whose physical chiral sector is recovered with controlled decoupling. For both a free-fermion Chern insulator and an interacting chiral spin liquid, the resulting PEPS show clean gapped correlation functions, and a finite transfer-matrix correlation length, in contrast with the artificial long-range tail of direct chiral PEPS representations. There exist small and negligibly coupling between the physical and auxiliary systems due to the finite entanglement effect, which only affect short-ranged local quantities. Despite the nonchiral enlarged representation, the chiral topological information remains encoded in the entanglement. Using layer-resolved momentum projection, we recover the expected universal chiral entanglement boundary spectrum. Our study provides a practical route to access gapped chiral phases with finite bond-dimension PEPS by changing the representation problem rather than directly studying the chiral pure state.

cond-mat.str-el↗

arXiv2025

Thermodynamic-Limit Evidence for Chiral Superconductivity Induced by Doping Chiral Topological Phases

The emergence of superconductivity from doping strongly correlated chiral topological phases in purely repulsive two-dimensional fermionic systems is a problem of broad and fundamental interest. However, existing numerical evidence has been limited to finite-size studies, and direct thermodynamic-limit evidence for superconducting long-range order has remained lacking. Here we provide such evidence for chiral superconductivity in the triangular Hofstadter-Hubbard model by advancing a simplex tensor-network approach that simultaneously captures superconducting long-range order and chiral topological order in the presence of intrinsic charge fluctuations, a capability that has remained challenging for previous two-dimensional approaches. We show that a broad intermediate-$U$ chiral spin liquid is separated from the weak-$U$ Chern insulator by a Mott transition, together forming undoped parent chiral topological states. Upon hole doping, we identify a uniform chiral superconducting state in the infinite system, characterized by a finite complex pairing order parameter. The pairing field exhibits an almost universal phase winding over a broad interaction-doping regime, with a distinct pocket of opposite winding near the Mott criticality. In addition, the entanglement spectrum retains the chiral structure of the parent topological phases while developing additional low-energy branches upon doping. These results establish that chiral superconductivity emerges robustly from doped chiral topological phases.

cond-mat.str-el↗

arXiv2025

Quantum anomalous Hall effects and emergent $\rm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene

Helical trilayer graphene realizes a versatile moir\'e system for exploring correlated topological states emerging from high Chern bands. Motivated by recent experimental observations of anomalous Hall effects at fractional fillings of magic-angle helical trilayers, we focus on the higher Chern number $|C_{band}|=2$ band and explore gapped many-body Hall states beyond the conventional Landau level paradigm. Through extensive exact diagonalization, we predict novel phases unattainable in a single $|C_{band}|=1$ band. At filling $\nu=2/3$ and $\nu=1/3$, a $\sqrt{3}\times \sqrt{3}$ charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance $|\sigma_{H}|=2e^2/3h$ are predicted respectively, indicating strong particle-hole asymmetry of the system. At half-filling $\nu=1/2$, an extensively degenerate pseudospin Hall ferromagnet featuring emergent $\rm{SU}(2)$ symmetry is found without the band being flat. Inspired by striking robustness of the ferromagnetic degeneracy, we develop a method to unveil and quantify the emergent symmetry via pseudospin operator construction in the presence of band dispersion and Coulomb interaction, and demonstrate persistence of the $\rm{SU}(2)$ quantum numbers even far away from the chiral limit. Incorporating spin-valley degrees of freedom, we identify an optimal filling regime $\nu_{\rm{total}}=3+\nu$ for realizing the above states. Notably, inter-flavor interactions renormalize the bandwidth and stabilize all the gapped phases even in realistic sublattice corrugation parameter regimes.

cond-mat.str-el↗

arXiv2024

Quantum phase diagram and non-abelian Moore-Read state in double twisted bilayer graphene

Experimental realizations of Abelian fractional Chern insulators (FCIs) have demonstrated the potentials of moir\'e systems in synthesizing exotic quantum phases. Remarkably, twisted multilayer graphene system may also host non-Abelian states competing with charge density wave under Coulomb interaction. Here, through larger scale exact diagonalization simulations, we map out the quantum phase diagram for $\nu=1/2$ system with electrons occupying the lowest moir\`e band of the double twisted bilayer graphene. By increasing the system size, we find the ground state has six-fold near degeneracy and with a finite spectral gap separating the ground states from excited states across a broad range of parameters. Further computation of many-body Chern number establish the topological order of the state, and we rule out possibility of charge density wave orders based on featureless density structure factor. Furthermore, we inspect the particle-cut entanglement spectrum to identify the topological state as a non-Abelian Moore-Read state. Combining all the above evidences we conclude that Moore-Read ground state dominates the quantum phase diagram for the double twisted bilayer graphene system for a broad range of coupling strength with realistic Coulomb interaction.

cond-mat.str-el↗

arXiv2024

Simulating chiral spin liquids with fermionic Projected Entangled Paired States

Chiral Spin Liquids (CSL) based on spin-1/2 fermionic Projected Entangled Pair States (fPEPS) are considered on the square lattice. First, fPEPS approximants of Gutzwiller-projected Chern insulators (GPCI) are investigated by Variational Monte Carlo (VMC) techniques on finite size tori. We show that such fPEPS of finite bond dimension can correctly capture the topological properties of the chiral spin liquid, as the exact GPCI, with the correct topological ground state degeneracy on the torus. Further, more general fPEPS are considered and optimized (on the infinite plane) to describe the CSL phase of a chiral frustrated Heisenberg antiferromagnet. The chiral modes are computed on the edge of a semi-infinite cylinder (of finite circumference) and shown to follow the predictions from Conformal Field Theory. In contrast to their bosonic analogs the (optimized) fPEPS do not suffer from the replication of the chiral edge mode in the odd topological sector.

cond-mat.str-el↗

arXiv2023

Chiral spin liquids with projected Gaussian fermionic entangled pair states

We study the parton construction of chiral spin liquids (CSLs) using projected Gaussian fermionic entangled pair states (GfPEPSs). First, we show that GfPEPSs can represent generic spinless Chern insulators faithfully with finite bond dimensions. Then, by applying the Gutzwiller projection to a bi-layer GfPEPSs, spin-1/2 Abelian and non-Abelian CSLs are obtained for Chern number $C=1$ and $C=2$, respectively. As a consequence of the topological obstruction for GfPEPSs, very weak Gossamer tails are observed in the correlation functions of the fermionic projected entangled pair state (PEPS) ansatze, suggesting that the no-go theorem for chiral PEPS is universal but does not bring any practical limitation. Remarkably, without fine tuning, all topological sectors can be constructed showing the expected number of chiral branches in the respective entanglement spectra, providing a sharp improvement with respect to the known bosonic PEPS approach.

cond-mat.str-el↗

arXiv2022

Chiral spin liquids on the kagome lattice with projected entangled simplex states

The infinite projected entangled simplex state (iPESS), a type of tensor network (TN) state, has been used successfully for simulating and characterizing {\it non-chiral} spin liquids on the kagome lattice. Here, we demonstrate that iPESS also provides a faithful representation of a {\it chiral} spin liquid (CSL) on the same lattice, namely the ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet with a scalar chirality. By classifying local tensors according to SU$(2)$ and point group symmetries, we construct a chiral ansatz breaking reflection $P$ and time reversal $T$ symmetries while preserving $PT$. The variational TN states are shown to host, for bond dimension $D\ge 8$, a chiral gapless entanglement spectrum following SU$(2)_1$ conformal field theory. The correlation function shows a small weight long-range tail complying with the prediction of the TN bulk-edge correspondence. %{\color{red}With more constraints included, the chiral ansatz is reduced to a non-chiral one which preserves full point group symmetries due to an emergent {\it tensor conservation law} and is of relevance to the ground state at the Heisenberg point. Lastly, by simulations in the complete ansatz family we discuss the transition from the non-chiral spin liquid to the CSL induced by the scalar chirality term.} We identify a non-chiral manifold spanned by only a subset of symmetric tensors where a new emergent {\it tensor conservation law} is realized. This allows us to both probe the stability of the non-chiral spin liquid and discuss its transition to CSL induced by a scalar chirality term.

cond-mat.str-el↗

arXiv2022

Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice

Motivated by recent experiments on Cs$_2$Cu$_3$SnF$_{12}$ and YCu$_{3}$(OH)$_{6}$Cl$_{3}$, we consider the ${S=1/2}$ Heisenberg model on the kagome lattice with nearest-neighbor super-exchange $J$ and (out-of-plane) Dzyaloshinskii-Moriya interaction $J_D$, which favors (in-plane) ${\bf Q}=(0,0)$ magnetic order. By using both variational Monte Carlo (based upon Gutzwiller-projected fermionic wave functions) and tensor-network approaches (built from infinite projected-entangled pair/simplex states), we show that the ground state develops a finite magnetization for $J_D/J \gtrsim 0.03 - 0.04$, while the gapless spin liquid remains stable for smaller values of the Dzyaloshinskii-Moriya interaction. The relatively small value of $J_D/J$ for which magnetic order sets in is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$. In addition, we assess the spin dynamical structure factors and the corresponding low-energy spectrum, by using the variational Monte Carlo technique. The existence of a continuum of excitations above the magnon modes is reported within the magnetically ordered phase, similarly to what has been detected by inelastic neutron scattering on Cs$_{2}$Cu$_{3}$SnF$_{12}$.

cond-mat.str-el↗

arXiv2021

Emergent gapless topological Luttinger liquid

Gapless Luttinger liquid is conventionally viewed as topologically trivial, unless it hosts degenerate ground states and or entanglement spectrum, which necessitates partial bulk degree of freedom to be gapped out. Here we predict an emergent gapless topological Luttinger liquid which is beyond the conventional scenarios and is characterized by the nontrivial many-body bulk spin texture, and propose feasible scheme for experimental observation. We consider a one-dimensional spin-orbit coupled Fermi-Hubbard model with fractional filling, whose low-energy physics is effectively described by a spinless Luttinger liquid and is trivial in the conventional characterization. We show that, as being tuned by the filling factor and interaction strength, the many-body ground state may exhibit nontrivial winding in its bulk spin texture in the projected momentum space, manifesting an emergent topological phase. A topological transition occurs when the projected spin-state at a high symmetry momentum becomes fully mixed one, resulting from competing processes of particle scattering to the lower and higher subbands, for which the spin texture at such momentum point is ill-defined, but the Luttinger liquid keeps gapless through the transition. Surprisingly, at relatively small filling the Luttinger liquid remains topologically nontrivial even at infinitely strong interaction. The results can be generalized to finite temperature which facilitates the real experimental detection. This work shows a novel gapless topological Luttinger liquid whose characterization is beyond the low-energy effective theory, and can be verified based on current experiments.

cond-mat.str-el↗

arXiv2020

Realization of ideal Weyl semimetal band in ultracold quantum gas with 3D Spin-Orbit coupling

The Weyl semimetals [1-6] are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band, and host massless quasiparticles known as Weyl fermions which were theorized by Hermann Weyl in the last twenties [7]. The lattice theory constrains that Weyl cones must come in pairs, with the minimal number of cones being two. The semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM) which is the optimal platform to explore broad Weyl physics but hard to engineer in solids. Here, we report the experimental realization of the IWSM band by synthesising for the first time a 3D spin-orbit (SO) coupling for ultracold atoms. Engineering a 3D configuration-tunable optical Raman lattice [8], we realize the Weyl type SO coupling for ultracold quantum gas, with which the IWSM band is achieved with controllability. The topological Weyl points are clearly measured via the virtual slicing imaging technique [8, 9] in equilibrium, and further resolved in the quench dynamics, revealing the key information of the realized IWSM bands. The realization of the IWSM band opens an avenue to investigate various exotic phenomena based on the optimal Weyl semimetal platforms.

cond-mat.quant-gas↗

arXiv2020

Realization and detection of non-ergodic critical phases in optical Raman lattice

The critical phases, being delocalized but non-ergodic, are fundamental phases which are different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose to realize such critical phases with and without interaction based on a topological optical Raman lattice scheme, which possesses one-dimensional spin-orbit coupling and an incommensurate Zeeman potential. We demonstrate the existence of both the noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail. Finally, we demonstrate how the proposed critical phases can be achieved based on the current cold atom experiments. This work paves the way to observe the novel critical phases.

cond-mat.str-el↗

arXiv2019

Emergent topology and symmetry-breaking order in correlated quench dynamics

Quenching a quantum system involves three basic ingredients: the initial phase, the post-quench target phase, and the non-equilibrium dynamics which carries the information of the former two. Here we propose a dynamical theory to characterize both the topology and symmetry-breaking order in correlated quantum system, through quenching the Haldane-Hubbard model from an initial magnetic phase to topologically nontrivial regime. The equation of motion for the complex pseudospin dynamics is obtained with the flow equation method, with the pseudospin evolution shown to obey a microscopic Landau-Lifshitz-Gilbert-Bloch equation. We find that the correlated quench dynamics exhibit robust universal behaviors on the so-called band-inversion surfaces (BISs), from which the nontrivial topology and magnetic order can be extracted. In particular, the topology of the post-quench regime can be characterized by an emergent dynamical topological pattern of quench dynamics on BISs, which is robust against dephasing and heating induced by interactions; the pre-quench symmetry-breaking orders is read out from a universal scaling behavior of the quench dynamics emerging on the BIS, which is valid beyond the mean-field regime. This work opens a way to characterize both the topology and symmetry-breaking orders by correlated quench dynamics.

cond-mat.quant-gas↗

arXiv2018

Observation of nodal-line semimetal with ultracold fermions in an optical lattice

Observation of topological phases beyond two-dimension (2D) has been an open challenge for ultracold atoms. Here, we realize for the first time a 3D spin-orbit coupled nodal-line semimetal in an optical lattice and observe the bulk line nodes with ultracold fermions. The realized topological semimetal exhibits an emergent magnetic group symmetry. This allows to detect the nodal lines by effectively reconstructing the 3D topological band from a series of measurements of integrated spin textures, which precisely render spin textures on the parameter-tuned magnetic-group-symmetric planes. The detection technique can be generally applied to explore 3D topological states of similar symmetries. Furthermore, we observe the band inversion lines from topological quench dynamics, which are bulk counterparts of Fermi arc states and connect the Dirac points, reconfirming the realized topological band. Our results demonstrate the first approach to effectively observe 3D band topology, and open the way to probe exotic topological physics for ultracold atoms in high dimensions.

cond-mat.quant-gas↗

arXiv2018

Magnetic effects on Chern Kondo insulator

We examine the Chern Kondo insulator proposed in a square optical lattice with staggered flux induced by $s$-$p$ orbital hybridization by revisiting its realization and taking into account the magnetic effects for the Kondo phases. The Ruderman-Kittel-Kasuya-Yoshida interaction is analyzed at the weak $s$-$p$ hybridization regime, with the anisotropic magnetic effects being discussed. Furthermore, the paramagnetic and magnetic phases coexisting with Kondo couplings are systematically investigated through the slave-boson theory, for which the rich phases are obtained, including the antiferromagnetic, collinear antiferromagnetic Kondo insulator, and Kondo metal phases. The magnetic orders are shown to enhance the effective Kondo hybridization compared with the case without taking into account magnetic effects, and exhibit different influences on the bulk topology. In particular, the antiferromagnetic order always enhances the topological phase by increasing bulk gap of the Chern Kondo phases. The results show the rich topological and magnetic effects obtained in the present Chern Kondo lattice model. We also investigate how to identify the topology and strong correlation effects through measuring the Hall conductance and double occupancy, which are achievable in ultracold atom experiments.

cond-mat.str-el↗

arXiv2018

Dynamical classification of topological quantum phases

Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete with ongoing challenges in both theory and experiment. Here we propose to establish a universal dynamical characterization of the topological quantum phases classified by integers, and further propose the high-precision dynamical schemes to detect such states. The framework of {the dynamical classification theory} consists of basic theorems. First, we uncover that classifying a $d$-dimensional ($d$D) gapped topological phase {of generic multibands} can reduce to a ($d-1$)D invariant defined on so-called band inversion surfaces (BISs), rendering a {\it bulk-surface duality} which simplifies the topological characterization. Further, we show in quenching across phase boundary the (pseudo)spin dynamics to exhibit unique topological patterns on BISs, which are attributed to the post-quench bulk topology and manifest a {\it dynamical bulk-surface correspondence}. For this the topological phase is classified by a dynamical topological invariant measured from dynamical spin-texture field on the BISs. Applications to quenching experiments on feasible models are proposed and studied, demonstrating the new experimental strategies to detect topological phases with high feasibility. This work opens a broad new direction to classify and detect topological phases by quantum dynamics.

cond-mat.mes-hall↗