arXiv subjects

Zhu-Xi Luo

Publications and source records attributed to Zhu-Xi Luo.

At least 19 recordsLinked to original sources

arXiv2026

Measures of Chirality in Mixed-State Topological Phases

What does it mean for a mixed-state topological phase to be chiral? Mathematically, chirality can be sharply characterized through the symmetry algebra of the mixed state. Physically, however, the question is far more subtle. In pure states, chirality in topological phase is tied to a web of familiar diagnostics, involving bulk-boundary correspondence, a gapless entanglement spectrum, a nontrivial modular commutator, and a quantized thermal Hall response. We show that none of these diagnostics remain reliable in mixed states. Instead, for decohered topological phases with a known error-free parent state, we propose two relative-entropy-based measures that can diagnose chirality, with one of them further extracting the chiral central charge. As a concrete example, we use these measures to analyze the $em^2$-decohered $\mathbb{Z}_3$ toric code, identifying the chirality transition to be in the random-bond Potts class for the particle-hole symmetric channel, and the polarized random bond Potts class for asymmetric channels. Our results emphasize how mixed-state topology demands intrinsically new diagnostics beyond direct analogues of pure-state probes.

quant-ph↗

arXiv2026

Entropic Barriers and the Kinetic Suppression of Topological Defects

Many quantum phases, from topological orders to superfluids, are destabilized at finite temperature by the proliferation and motion of topological defects such as anyons or vortices. Conventional protection mechanisms rely on energetic gaps and fail once thermal fluctuations exceed the gap scale. Here we examine a complementary mechanism of entropic protection, in which defect nucleation is suppressed by coupling to mesoscopic auxiliary reservoirs of dimension $M$, generating an effective free-energy barrier that increases with temperature. In the Ising chain, this produces a characteristic three-regime evolution of the correlation length as a function of temperature - linear growth, entropy-controlled plateau, and eventual breakdown - indicating a general modification of defect behavior. Focusing on two spatial dimensions, where true finite-temperature topological order is forbidden in the thermodynamic limit, we show that entropic protection can nevertheless strongly enhance stabilization at finite system size, the regime directly relevant for quantum memory and experiments. Owing to the topological character of the defects, creation and transport are independently suppressed, yielding a double parametric reduction of logical errors in the entropic toric code and enhanced coherence when the framework is extended to Berezinskii-Kosterlitz-Thouless transitions. Entropic barriers thus provide a passive and scalable route to stabilizing quantum phases in experimentally relevant regimes. We propose an experimental setup for entropic toric code using dual species Rydberg arrays with dressing.

quant-ph↗

arXiv2026

Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems

Strong-to-weak spontaneous symmetry breaking (SWSSB) defines a mixed-state phase of matter--without a pure-state counterpart--in which nonlinear observables such as the Rényi-2 correlator develop long-range order while conventional linear correlations remain short-ranged. Here we study the emergence of SWSSB in one-dimensional open quantum systems governed by Lindbladian evolution, where the transition time diverges with system size and SWSSB appears only asymptotically in the steady state. By tracking the late-time growth of the Rényi-2 correlation length, we uncover a universal dynamical regime controlled purely by the symmetry class of the Lindbladian. Contrary to the conventional expectation that late-time dynamics are governed by the low-lying Liouvillian spectrum, we find that the time dependence of the SWSSB transition--exponential versus algebraic--is dictated solely by symmetry, independent of details of the Lindbladian, including whether the Liouvillian spectrum is gapped or gapless. For $\mathbb{Z}_2$-symmetric dynamics, the Rényi-2 correlation length grows exponentially in time--even when the spectrum is gapless--yielding an effective transition time $t_c \propto \operatorname{ln} L$ and enabling rapid preparation of the $\mathbb{Z}_2$ SWSSB steady state. In contrast, U(1)-symmetric dynamics exhibit algebraic scaling, $t_c \propto L^α$, with a filling-dependent dynamical exponent: ballistic growth ($α\approx 1$) at finite filling crosses over to diffusive scaling ($α= 2$) in the zero-filling limit. These results establish symmetry--rather than spectral gap structure--as the controlling principle for SWSSB late-time dynamical scaling, and open a new route to nonequilibrium symmetry breaking in open quantum systems.

cond-mat.mes-hall↗

arXiv2026

Moiré in $Γ$-valley square lattice: Copper- and iron-based superconductor simulation in a single device

Novel superconducting phases have been found in various moiré heterostructures based on hexagonal lattices. However, the archetypal high-temperature superconductors (cuprates, iron-based and nickelate families) all share a square lattice foundation. These materials host a rich landscape of correlated phenomena, such as charge and spin stripes, pseudogap behavior, and unconventional metallicity, which continue to challenge our fundamental understanding of strongly correlated electrons. In this work, we investigate the possibility of simulating the effective models governing these high-$T_c$ superconductors using twisted homobilayers of $Γ$-valley square-lattice systems. We develop a universal theoretical framework and carry out a detailed analysis of a promising candidate material ZnF$_2$. We find that the first moiré band realizes a single-orbital square-lattice Hubbard model, widely believed to capture cuprate physics, while the second and third moiré bands map to a $p_x,p_y$ two-orbital square-lattice Hubbard model, which shares common physics to the minimal $d_{xz}, d_{yz}$ models proposed for iron pnictides. Our study combines continuum Hamiltonian modeling, first-principle calculations, and Hartree-Fock mean field theory. The latter focuses on the quarter-filling regime of the two-orbital model and in particular leads to, among others, a stable antiferro-orbital, ferromagnetic insulating phase. These results highlight $Γ$-valley square-lattice moiré systems as a new and important generation of van der Waals heterostructures to realize interesting strongly correlated phases of matter.

cond-mat.str-el↗

arXiv2026

Strong-to-weak spontaneous breaking of 1-form symmetry and intrinsically mixed topological order

Topological orders in 2+1d are spontaneous symmetry-breaking (SSB) phases of 1-form symmetries in pure states. The notion of symmetry is further enriched in the context of mixed states, where a symmetry can be either ``strong" or ``weak". In this work, we apply a Rényi-2 version of the proposed equivalence relation in [Sang, Lessa, Mong, Grover, Wang, & Hsieh, to appear] on density matrices that is slightly finer than two-way channel connectivity. This equivalence relation distinguishes general 1-form strong-to-weak SSB (SW-SSB) states from phases containing pure states, and therefore labels SW-SSB states as ``intrinsically mixed". According to our equivalence relation, two states are equivalent if and only if they are connected to each other by finite Lindbladian evolution that maintains continuously varying, finite Rényi-2 Markov length. We then examine a natural setting for finding such density matrices: disordered ensembles. Specifically, we study the toric code with various types of disorders and show that in each case, the ensemble of ground states corresponding to different disorder realizations form a density matrix with different strong and weak SSB patterns of 1-form symmetries, including SW-SSB. Furthermore we show by perturbative calculations that these disordered ensembles form stable ``phases" in the sense that they exist over a finite parameter range, according to our equivalence relation.

quant-ph↗

arXiv2026

The source of hardware-tailored codes and coding phases

A central challenge in quantum error correction is identifying powerful quantum codes tailored to specific hardware and determining their error thresholds above which quantum information is unprotected. This problem is hard because we cannot determine the noise models for our devices. Inspired by the quantum capacity theorem, we seek an optimal quantum source of information, namely the density matrix that degrades minimally when passed through a noisy channel. We explore this idea with the Open Random Unitary Model (ORUM), a simplified model of a $N$-qubit quantum computer with competing depolarizing and dephasing channels as a stand-in for unitary gates and measurements. Through numerical optimization, we find that the ORUM hosts three discrete regimes, three "phases", the "maximally mixed source" phase, a "$\mathbb{Z}_2$ source" phase (where ORUM's $U(1)$ gauge symmetry is broken down to $\mathbb{Z}_2$), and a no-coding phase where all information is lost. These phases exhibit first-order transitions among themselves and converge at a novel zero-capacity multicritical point. These results show a remarkable similarity between the quantum capacity theorem and Jaynes' maximum entropy principle of statistical mechanics. Using the $\mathbb{Z}_2$ source, we build two codes, a classical cat code capable of correcting all the dephasing errors and a concatenated cat code capable of correcting all errors up to a distance $d=\text{min}(m,N)$ and reduces to Shor's 9-qubit code for $m=N=3$. Neither classical nor quantum code survives near the vicinity of the zero-capacity multicritical point in the source phase diagram. Applying our approach to current noisy devices could provide a systematic method for constructing quantum codes for robust computation and communication.

quant-ph↗

arXiv2025

Single-band square lattice Hubbard model from twisted bilayer C568

We propose twisted homobilayer of a carbon allotrope, C$_{568}$, to be a promising platform to realize controllable square lattice single-band extended Hubbard model. This setup has the advantage of a widely tunable $t'/t$ ratio without adding external fields, and the intermediate temperature $t\ll T\ll U$ regime can be easily achieved. We first analyze the continuum model obtained from symmetry analysis and first-principle calculations, and calculate the band structures. Subsequently, we derive the corresponding tight-binding models and fit the hopping parameters as well as the Coulomb interactions. When displacement field is applied, anisotropic nearest neighbor hoppings can further be achieved. If successfully fabricated, the device could be an important stepping stone towards understanding high-temperature superconductivity.

cond-mat.str-el↗

arXiv2025

Tensor Network Representations for Intrinsically Mixed-State Topological Orders

Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor network representations for intrinsically mixed-state topological phases, which exhibit nontrivial topological phenomena and do not have pure-state counterparts. The method exploits the power of anyon condensation in Choi states and is applicable to the cases where the target states arise from pure-state topological phases subject to strong decoherence/disorders in the Abelian sectors. Representative examples include $m^a e^b$ decoherence of $\mathbb{Z}_N$ toric code, decohered non-Abelian $S_3$ quantum double as well as pure $Z$/$X$ decoherence of arbitrary CSS codes. An example of chiral topological phases which cannot arise from local commuting projector models are also presented.

cond-mat.str-el↗

arXiv2025

Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit

Symmetry is a powerful tool for understanding phases of matter in equilibrium. Quantum circuits with measurements have recently emerged as a platform for novel states of matter intrinsically out of equilibrium. Can symmetry be used as an organizing principle for these novel states, their phases and phase transitions? In this work, we give an affirmative answer to this question in a simple adaptive monitored circuit, which hosts an ordering transition in addition to a separate entanglement transition, upon tuning a single parameter. Starting from a symmetry-breaking initial state, depending on the tuning parameter, the steady state could (i) remain symmetry-broken, (ii) exhibit the average symmetry in the ensemble of trajectories, or (iii) exhibit the exact symmetry for each trajectory. The ordering transition is mapped to the transition in a classical majority vote model, described by the Ising universality class, while the entanglement transition lies in the percolation class. Numerical simulations are further presented to support the analytical understandings.

quant-ph↗

arXiv2025

Tunable $t-t'-U$ Hubbard models in twisted square homobilayers

Square lattice Hubbard models with tunable hopping ratio $t'/t$ are highly promising for realizing a variety of quantum phases and for shedding light on key puzzles in correlated quantum materials, including higher-temperature superconductivity. We show that twisted square lattice homo-bilayers generically offer such tunability when the flat bands originate from the corner of the Brillouin zone. We reveal an emergent symmetry at low twist-angles, absent in single layers, that necessitates the vanishing of nearest neighbor hopping ($t=0$). This symmetry can be lifted by an inter-layer displacement field or by an in-plane magnetic field, introducing tunable $t$ and anisotropy, allowing access to a wide range of $t'/t$ ratios for correlated electrons on a moiré square lattice.

cond-mat.str-el↗

arXiv2025

Entanglement renormalization of fractonic anisotropic $\mathbb{Z}_N$ Laplacian models

Gapped fracton phases constitute a new class of quantum states of matter which connects to topological orders but does not fit easily into existing paradigms. They host unconventional features such as sub-extensive and robust ground state degeneracies as well as sensitivity to lattice geometry. We investigate the anisotropic $\mathbb{Z}_N$ Laplacian model [1] which can describe a family of fracton phases defined on arbitrary graphs. Focusing on representative geometries where the 3D lattices are extensions of 2D square, triangular, honeycomb and Kagome lattices into the third dimension, we study their ground state degeneracies and mobility of excitations, and examine their entanglement renormalization group (ERG) flows. All models show bifurcating behaviors under ERG but have distinct ERG flows sensitive to both $N$ and lattice geometry. In particular, we show that the anisotropic $\mathbb{Z}_N$ Laplacian models defined on the extensions of triangular and honeycomb lattices are equivalent when $N$ is coprime to $3$. We also point out that, in contrast to previous expectations, the model defined on the extension of Kagome lattice is robust against local perturbations if and only if $N$ is coprime to $6$.

cond-mat.str-el↗

arXiv2025

A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice

Early studies proposed a connection between cuprate superconductivity and fractionalized spin liquid states. But the low temperature phase diagram is dominated by states without fractionalization, with a competition between superconductivity and charge-ordered states which break translational symmetry. Our theory uncovers novel features associated with a particular spin-liquid presumed to underlie the pseudogap metal, and shows that it has multiple nearly-degenerate instabilities to confinement of fractionalized excitations, leading to antiferromagnetism, $d$-wave superconductivity, and/or charge order. Our theory provides routes to resolving a number of open puzzles on the cuprate phase diagram. The spin liquid is described by a SU(2) gauge theory of $N_f=2$ massless fundamental Dirac fermions, has an emergent SO(5)$_f$ global symmetry, and is presumed to confine at low energies to the Néel state. At non-zero doping (or smaller Hubbard repulsion at half-filling) we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges moving in $π$ flux. At half-filling, the low energy Higgs sector has $N_b=2$ relativistic bosons with a possible emergent SO(5)$_b$ global symmetry describing rotations between a $d$-wave superconductor, period-2 charge stripes, and the time-reversal breaking `$d$-density wave' state. We propose a deconfined quantum critical point between a confining state which breaks SO(5)$_f$ and a confining state which breaks SO(5)$_b$. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and $d$-wave superconductivity. A similar theory applies at non-zero doping and large $U$, with longer-range couplings of the chargons leading to charge order with longer periods.

cond-mat.str-el↗

arXiv2024

Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the $π$-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background $π$-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal $d$-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases which are very likely described by 2+1 dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional $d$-wave superconductor with gapless Bogoliubov quasiparticles at 4 nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semi-metal phases.

cond-mat.str-el↗

arXiv2023

Anomalies of Average Symmetries: Entanglement and Open Quantum Systems

Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.

cond-mat.str-el↗

arXiv2023

Universal relations for holographic interfaces

We study the entanglement entropy in 1+1 dimensional conformal field theories in the presence of interfaces from a holographic perspective. Compared with the well-known case of boundary conformal field theories, interfaces allow for several interesting new observables. Depending on how the interface is located within the entangling region, the entanglement entropies differ and exhibit surprising new patterns and universal relations. While our analysis is performed within the framework of holography, we expect our results to hold more generally.

hep-th↗

arXiv2023

Gapped Interfaces in Fracton Models and Foliated Fields

This work investigates the gapped interfaces of 3+1d fracton phases of matter using foliated gauge theories and lattice models. We analyze the gapped boundaries and gapped interfaces in X cube model, and the gapped interfaces between the X-cube model and the toric code. The gapped interfaces are either "undecorated" or "decorated", where the "decorated" interfaces have additional Chern-Simons like actions for foliated gauge fields. We discover many new gapped boundaries and interfaces, such as (1) a gapped boundary for X-cube model where the electric lineons orthogonal to the interface become the magnetic lineons, the latter are the composite of magnetic planons; (2) a Kramers-Wannier-duality type gapped interface between the X-cube model and the toric code model from gauging planar subsystem one-form symmetry; and (3) an electromagnetic duality interface in the X-cube model that exchanges the electric and magnetic lineons.

cond-mat.str-el↗

arXiv2023

Mott insulators in moiré transition metal dichalcogenides at fractional fillings: Slave-rotor mean-field theory

In this work, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moiré systems, that captures both the formation of Wigner crystals as well as exotic spin states on top of these charge backgrounds. Phase diagrams are mapped out for different choices of long-range Coulomb repulsion strength, reproducing several experimentally found Wigner crystal states. Assuming unbroken time reversal symmetry, we find several spin liquid states as well as dimer states at fractional fillings. While spin dimer states are always found to have the lowest mean field energy, several spin liquid states are energetically competitive and may be stabilized by including gauge fluctuations or further interaction terms. We further discuss possible experimental signatures of these states pertinent to two-dimensional moiré heterostructures.

cond-mat.str-el↗

arXiv2022

Gapped boundaries of (3+1)d topological orders

Given a gapped boundary of a (3+1)d topological order (TO), one can stack on it a decoupled (2+1)d TO to get another boundary theory. Should one view these two boundaries as "different"? A natural choice would be no. Different classes of gapped boundaries of (3+1)d TO should be defined modulo these decoupled (2+1)d TOs. But is this enough? We examine the possibility of coupling the boundary of a (3+1)d TO to additional (2+1)d TOs or fractonic systems, which leads to even more possibilities for gapped boundaries. Typically, the bulk point-like excitations, when touching the boundary, become excitations in the added (2+1)d phase, while the string-like excitations in the bulk may end on the boundary but with endpoints dressed by some other excitations in the (2+1)d phase. For a good definition of "class" for gapped boundaries of (3+1)d TO, we choose to quotient out the different dressings as well. We characterize a class of gapped boundaries by the string-like excitations that can end on the boundary, whatever their endpoints are. A concrete example is the (3+1)d bosonic toric code. Using group cohomology and category theory, three gapped boundaries have been found previously: rough boundary, smooth boundary and twisted smooth boundary. We can construct many more gapped boundaries beyond these, which all naturally fall into two classes corresponding to whether the $m$-string can or cannot end on the boundary. According to this classification, the previously found three boundaries are grouped as {rough}, {smooth, twisted smooth}. For a (3+1)d TO characterized by a finite group $G$, different classes correspond to different subgroups of $G$. We illustrate the physical picture from various perspectives including coupled layer construction, Walker-Wang model and field theory.

cond-mat.str-el↗