arXiv subjects

Biao Lian

Publications and source records attributed to Biao Lian.

At least 19 recordsLinked to original sources

arXiv2026

Translationally Covariant Modulated Symmetries: Classification and Goldstone

Modulated symmetries are global symmetries with a spatially dependent unit of charge, such as the dipole symmetry and the exponential symmetry. We give the generic condition for a modulated symmetry to be compatible with translationally symmetric Hamiltonians, which we define as a translationally covariant modulated symmetry (TCMS). For Abelian TCMSs, we prove that their units of charge can only contain multipole, exponential and harmonic components. Particularly, we classify all the one-dimensional TCMSs by real Jordan normal form blocks. We further derive the generic Goldstone action for SSB phases of continuous TCMSs, by which we show that a broken multipole symmetry gives higher-order gapless Goldstone modes, a broken harmonic symmetry gives gapless Goldstone modes at finite momenta, and a broken exponential symmetry gives no gapless Goldstone modes, modifying the conventional Goldstone theorem.

cond-mat.str-el↗

arXiv2026

Bridging Commutant and Polynomial Methods for Hilbert Space Fragmentation

A quantum model exhibits Hilbert space fragmentation (HSF) if its Hilbert space decomposes into exponentially many dynamically disconnected subspaces, known as Krylov subspaces. A model may however have different HSFs depending on the method for identifying them. Here we establish a connection between two vastly distinct methods recently proposed for identifying HSF: the commutant algebra (CA) method and integer characteristic polynomial factorization (ICPF) method. For a Hamiltonian consisting of operators admitting rational number matrix representations, we prove a theorem that, if its center of commutant algebra have all eigenvalues being rational, the HSF from the ICPF method must be equal to or finer than that from the CA method. We show that this condition is satisfied by most known models exhibiting HSF, for which we demonstrate the validity of our theorem. We further discuss representative models for which ICPF and CA methods yield different HSFs. Our results may facilitate the exploration of a unified definition of HSF.

cond-mat.stat-mech↗

arXiv2025

Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass

We study the phase diagram of a one-dimensional spin quantum breakdown model, which has an exponential $U(1)$ symmetry with charge unit decaying as $2^{-j}$ with site position $j$. By exact diagonalization and density matrix renormalization group, we show that the model with spin $S\ge2$ exhibits an exponential $U(1)$ spontaneous symmetry-breaking (SSB) phase dubbed a quantum breakdown condensate. It exhibits a bulk gap violating the Goldstone theorem, and an edge mode only on the left edge if in open boundary condition. In a length $L$ lattice, the condensate has $\mathcal{O}(2^L)$ number of SSB ground states originating from the $\mathcal{O}(2^L)$ number of exponential $U(1)$ charge sectors, leading to a finite entropy density $\ln 2$. This enforces a first-order SSB phase transition into this phase, as observed numerically and verified in the large $S$ limit on an exactly solvable Rokhsar-Kivelson line. The condensate has an SSB order parameter being the local in-plane spin, which points in angles related by the chaotic Bernoulli (dyadic) map and thus is effectively random. Moreover, we show the condensate exhibits nondecaying local autocorrelations, and does not have an off-diagonal long-range order. The quantum breakdown condensate thus behaves as a disorder-free quantum glass and is beyond the existing classifications of phases of matter.

cond-mat.str-el↗

arXiv2025

Bosonic Quantum Breakdown Hubbard Model

We propose a bosonic quantum breakdown Hubbard model, which generalizes the Bose-Hubbard model by adding an asymmetric breakdown interaction turning one boson into two between adjacent sites. When the normal hopping is zero, this model has a global exponential U(1) symmetry, and we show that the ground state undergoes a first-order phase transition from a Mott insulator (MI) to a spontaneously symmetry breaking (SSB) breakdown condensate as the breakdown interaction increases. Surprisingly, the SSB breakdown condensate does not have a gapless Goldstone mode, which invalidates the Mermin-Wagner theorem and leads to stable SSB in one dimension. Moreover, we show that the quench dynamics of a boson added to MI exhibits a dynamical transition from dielectric to breakdown phases, which happens at a larger breakdown interaction than the ground state phase transition. Between these two transitions, the MI (dielectric) state is a false vacuum stable against dynamical breakdown. Our results reveal that quantum models with unconventional symmetries such as the exponential symmetry can exhibit unexpected properties.

cond-mat.str-el↗

arXiv2025

Wilson-Loop-Ideal Bands and General Idealization

Quantum geometry is universally bounded from below by Wilson-loop windings. In this work, we define an isolated set of bands to be Wilson-loop-ideal, if their quantum metric saturates the Wilson-loop lower bound. The definition naturally incorporates the known Chern-ideal and Euler-ideal bands, and allows us to define other types of ideal bands, such as Kane-Mele $Z_2$-ideal and inversion-fragile-ideal bands. In particular, we find that in the case of zero total Chern number, an isolated WL-ideal set of two bands with non-singular nonabelian Berry curvature and nontrivial normal Wilson-loop winding always admits a Chern-ideal gauge, without the need of a global good quantum number (such as spin). This enables the direct construction of new topologically ordered states, such as fractional topological insulator wavefunctions. We further propose a general framework of constructing monotonic flows that achieve Wilson-loop-ideal states starting from non-ideal bands through band mixing, where Wilson-loop-ideal states are not energy eigenstates but have smooth projectors similar to isolated bands. We apply the constructed flows to the realistic model of $3.89^\circ$ twisted bilayer MoTe$_2$, a moir\'e Rashba model and another moir\'e time-reversal-breaking models, and numerically find Chern-ideal, $Z_2$-ideal and inversion-fragile states, respectively, with relative error in the integrated quantum metric below $5\times 10^{-3}$. Our exact-diagonalization calculations on the numerically ideal states demonstrate the potential of our general definition of Wilson-loop-ideal bands and general procedure of constructing Wilson-loop-ideal states for future study of novel correlated physics.

cond-mat.mes-hall↗

arXiv2025

Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries

We develop a method to calculate generic time-dependent correlation functions for inhomogeneous quantum quenches in (1+1)-dimensional conformal field theory (CFT) induced by sudden Hamiltonian deformations that modulate the energy density inhomogeneously. Our work particularly focuses on the effects of spatial boundaries, which have remained unresolved by previous analytical methods. For generic post-quench Hamiltonian, we develop a generic method to calculate the correlations by mirroring the system, which otherwise are Euclidean path integrals in complicated spacetime geometries difficult to calculate. On the other hand, for a special class of inhomogeneous post-quench Hamiltonians, including the Möbius and sine-square-deformation Hamiltonians, we show that the quantum quenches exhibit simple boundary effects calculable from Euclidean path integrals in a straightforward strip spacetime geometry. Applying our method to the time evolution of entanglement entropy, we find that for generic cases, the entanglement entropy shows discontinuities (shockwave fronts) propagating from the boundaries.In contrast, such discontinuities are absent in cases with simple boundary effects. We verify that our generic CFT formula matches well with numerical calculations from free fermion tight-binding models for various quench scenarios.

cond-mat.stat-mech↗

arXiv2025

Quantized Transport of $\nu = 2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity

Quantum Hall edge states in proximity to a superconductor (SC) usually acquire a non-quantized electron-to-hole conversion probability in transport, due to non-universal SC couplings and disorders. With counter-propagating modes, we show that the situation can be the opposite in the $\nu=2/3$ fractional quantum Hall (FQH) edge states with SC proximity, where disordered SC-couplings can reconstruct the edge states into an infinite set of stable phases with quantized electron-to-hole conversion probability along a long edge. Each phase is dominated by a disordered SC-coupling that tunnels $\pm |q_N|$ Cooper pairs, which can take values $|q_N|=1, 4, 15$, etc. We predict that this gives rise to a quantized downstream resistance $R_d = h/(2q^2_Ne^2)$ in an FQH-SC junction, serving as a quantized electrical transport signature beyond the Hall conductance. Higher-order nonlinear transport due to irrelevant Cooper pair tunneling or vortex dissipation is further studied, which becomes dominant when the edge is in a normal phase. Our results apply to both the single-layer state (as a particle-hole conjugate of $\nu=1/3$) and the bilayer Halperin-(112) state, revealing a rich landscape of disorder-stabilized phases in FQH edge states with SC proximity, and may as well apply to fractional Chern insulators recently observed at the same filling.

cond-mat.mes-hall↗

arXiv2025

Intervalley-Coupled Twisted Bilayer Graphene from Substrate Commensuration

We show that intervalley coupling can be induced in twisted bilayer graphene (TBG) by aligning the bottom graphene layer with either of two types of commensurate insulating triangular Bravais lattice substrate. The intervalley coupling folds the $\pm K$ valleys of TBG to the $\Gamma$-point and hybridizes the original TBG flat bands into a four-band model equivalent to the $p_x$-$p_y$ orbital honeycomb lattice model, in which the second conduction and valence bands have quadratic band touchings and can become flat due to geometric frustration. The spin-orbit coupling from the substrate opens gaps between the bands, yielding topological bands with spin Chern numbers $\mathcal{C}$ up to $\pm 4$. For realistic substrate potential strengths, the minimal bandwidths of the hybridized flat bands are still achieved around the TBG magic angle $\theta_M=1.05^\circ$, and their quantum metrics are nearly ideal. We identify two candidate substrate materials Sb$_2$Te$_3$ and GeSb$_2$Te$_4$, which nearly perfectly realize the commensurate lattice constant ratio of $\sqrt{3}$ with graphene. These systems provide a promising platform for exploring strongly correlated topological states driven by geometric frustration.

cond-mat.mes-hall↗

arXiv2025

Two-dimensional quantum breakdown model with Krylov subspace many-body localization

We propose a two-dimensional (2d) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set of subsystem symmetries, and has a strong fragmentation into Krylov subspaces in each symmetry sector. The Hamiltonian in each Krylov subspace maps to a single-particle problem in a Cayley tree-like graph. At zero disorder, the Krylov subspaces exhibit either (possible) integrable features, or quantum chaos with quantum scar states showing irregular energy and degeneracy patterns. At nonzero disorders, they enter a 2d many-body localization (MBL) phase beyond certain disorder strength $W_*$, as indicated by Poisson level spacing statistics and entanglement entropy growing as $\log t$ with time $t$. Our theoretical arguments suggest $W_*$ is finite or zero for boson number $N_b\lesssim L^γ/\log L$ ($1/2\le γ\le 1$) as system size $L\rightarrow\infty$. This gives a more stringent condition for MBL than that in the 1d quantum breakdown models. This model reveals the possibility of MBL in systems of quantum particles interacting with classical degrees of freedom.

cond-mat.str-el↗

arXiv2025

Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model

We introduce a dissipative lattice gauge model that exhibits the many-body version of the non-Hermitian skin effect. The dissipative couplings between dynamical gauge fields on the lattice links and the surrounding environment generate chiral motions of particles residing on lattice sites. Despite the complexity arising from many-body interactions, the local gauge symmetry enables the exact construction of a steady state that displays the many-body non-Hermitian skin effect. Furthermore, our approach can be generalized to realize a new type of many-body non-Hermitian skin effect, dubbed the hierarchical skin effect, where different subsystem degrees of freedom exhibit boundary accumulation of multiple moments at different orders. Our findings can be readily observed by engineering dissipation in state-of-the-art lattice gauge simulators.

quant-ph↗

arXiv2025

Spectroscopy of the Fractal Hofstadter Energy Spectrum

Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux quanta per lattice unit cell, this spectrum shows self-similar distributions of energy levels that reflect its recursive construction. For most materials, Hofstadter's butterfly is predicted under experimental conditions that are unachievable using laboratory-scale magnetic fields. More recently, electrical transport studies have provided evidence for Hofstadter's butterfly in materials engineered to have artificially large lattice constants, such as those with moiré superlattices. Yet to-date, direct spectroscopy of the fractal energy spectrum predicted by Hofstadter nearly 50 years ago has remained out of reach. Here we use high-resolution scanning tunneling microscopy / spectroscopy (STM / STS) to probe the flat electronic bands in twisted bilayer graphene near the predicted second magic angle, an ideal setting for spectroscopic studies of Hofstadter's spectrum. Our study shows the fractionalization of flat moiré bands into discrete Hofstadter subbands and discerns experimental signatures of self-similarity of this spectrum. Moreover, our measurements uncover a spectrum that evolves dynamically with electron density, displaying phenomena beyond that of Hofstadter's original model due to the combined effects of strong correlations, Coulomb interactions, and the quantum degeneracy of electrons in twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2024

Emergent Symmetry and Valley Chern Insulator in Twisted Double-Bilayer Graphene

Theoretical calculations show that twisted double bilayer graphene (TDBG) under a transverse electric field develops a valley Chern number 2 at charge neutrality. Using thermodynamic and thermal activation measurements we report the experimental observation of a universal closing of the charge neutrality gap in the Hofstadter spectrum of TDBG at 1/2 magnetic flux per unit cell, in agreement with theoretical predictions for a valley Chern number 2 gap. Our theoretical analysis of the experimental data shows that the interaction energy, while larger than the flat-band bandwidth in TDBG near 1°does not alter the emergent valley symmetry or the single-particle band topology.

cond-mat.mes-hall↗

arXiv2024

Twisted coupled wire model for a moiré sliding Luttinger liquid

Recent experiments in twisted bilayer WTe$_2$ revealed the existence of anisotropic Luttinger liquid behavior. To generically characterize such anisotropic twisted bilayer systems, we study a model of a twisted bilayer of two-dimensional (2D) arrays of coupled wires, which effectively form an array of coupled moiré wires. We solve the model by the transfer matrix method, and identify quasi-1D electron bands in the system at small twist angles. With electron interactions added, we show that the moiré wires have an effective Luttinger parameter $g_\text{eff}$ much lower than that of the microscopic wires. This leads to a sliding Luttinger liquid (SLL) temperature regime, in which power-law current voltage relations arise. For parameters partly estimated from WTe$_2$, a microscopic interaction $U\sim0.7$eV yields a temperature regime of SLL similar to that in the WTe$_2$ experiments.

cond-mat.str-el↗

arXiv2024

Correlated topological flat bands in rhombohedral graphite

Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger (SSH) model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon {\it in situ} electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a new platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.

cond-mat.str-el↗

arXiv2024

Electron phonon coupling in the topological heavy fermion model of twisted bilayer graphene

On flat bands of the magic-angle twisted bilayer graphene, exotic correlation physics unfolds. Phonons, through mediating an effective electron-electron interaction, can play a crucial role in selecting various electronic phases. In this study, we derive the full electron-phonon coupling (EPC) vertex from the microscopic tight-binding lattice, and identify the significance of each phonon mode. We then project the EPC vertices onto the topological heavy fermion (THF) basis [Song and Bernevig, Phys. Rev. Lett. 129, 047601 (2022)], and show that an anti-Hund's interaction $\hat{H}_{\rm A}$ is induced on each moiré-scale local $f$-orbital, with strengths 1 to 4 meV. We analyze the phonon-induced multiplet splittings, which can significantly affect the local correlation. As an example, we elaborate on the phonon-favored symmetry-breaking orders at even-integer fillings. Through systematic self-consistent Hartree-Fock calculations, we uncover a tight competition between $Γ$-phonon-favored orbital orders, $K$-phonon-favored inter-valley coherent orders, and the kinetic and Coulomb-favored orders. Contrary to EPC, the carbon atom Hubbard repulsion induces an on-$f$-site Hund's interaction $\hat{H}_{\rm H}$ with strengths 1 to 3 meV that partly counteracts the effect of $\hat{H}_{\rm A}$. The combined influence of $\hat{H}_{\rm A,H}$ on the multiplet splitting and symmetry-breaking states is discussed. In the end, we explore the possibility of finding an exotic Dirac semi-metal formed solely by $c$-electrons at the charge-neutrality point, while $f$-impurities exhibit a symmetric Mott gap by forming non-degenerate singlets under $\hat{H}_{\rm A,H}$. Experimental features that distinguish such a state are discussed.

cond-mat.str-el↗

arXiv2024

Entanglement Entropy of Free Fermions in Timelike Slices

We define the entanglement entropy of free fermion quantum states in an arbitrary spacetime slice of a discrete set of points, and particularly investigate timelike (causal) slices. For 1D lattice free fermions with an energy bandwidth $E_0$, we calculate the time-direction entanglement entropy $S_A$ in a time-direction slice of a set of times $t_n=nτ$ ($1\le n\le K$) spanning a time length $t$ on the same site. For zero temperature ground states, we find that $S_A$ shows volume law when $τ\ggτ_0=2π/E_0$; in contrast, $S_A\sim \frac{1}{3}\ln t$ when $τ=τ_0$, and $S_A\sim\frac{1}{6}\ln t$ when $τ<τ_0$, resembling the Calabrese-Cardy formula for one flavor of nonchiral and chiral fermion, respectively. For finite temperature thermal states, the mutual information also saturates when $τ<τ_0$. For non-eigenstates, volume law in $t$ and signatures of the Lieb-Robinson bound velocity can be observed in $S_A$. For generic spacetime slices with one point per site, the zero temperature entanglement entropy shows a clear transition from area law to volume law when the slice varies from spacelike to timelike.

cond-mat.stat-mech↗

arXiv2024

From the Quantum Breakdown Model to the Lattice Gauge Theory

The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including many-body localization and quantum chaos with quantum scar states. We investigate the minimal quantum breakdown model with the minimal number of on-site fermion orbitals required for the interaction, and identify a large number of local conserved charges in the model. We then reveal a mapping between the minimal quantum breakdown model in certain charge sectors and a quantum link model which simulates the U(1) lattice gauge theory, and show that the local conserved charges map to the gauge symmetry generators. A special charge sector of the model further maps to the PXP model, which shows quantum many-body scars. This mapping unveils the rich dynamics in different Krylov subspaces characterized by different gauge configurations in the quantum breakdown model.

cond-mat.str-el↗

arXiv2024

Molecular Pairing in Twisted Bilayer Graphene Superconductivity

We propose a theory for how the weak phonon-mediated interaction ($J_{\rm A}\!=\!1\!\sim\!4$meV) wins over the prohibitive Coulomb repulsion ($U\!=\!30\!\sim\!60$meV) and leads to a superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A$_3$C$_{60}$ family of molecular superconductors: Each AA stacking region of MATBG resembles a C$_{60}$ molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced $J_{\rm A}$ has the form of an inter-valley anti-Hund's coupling and is less suppressed than $U$ by the Kondo screening near a Mott insulator. Additionally, we also considered an intra-orbital Hund's coupling $J_{\rm H}$ that originates from the on-site repulsion of a carbon atom. Under a reasonable approximation of the realistic model, we prove that the renormalized local interaction between quasi-particles must have a pairing (negative) channel in a doped correlated insulator at $ν=\pm(2+δν)$, albeit the bare interaction is positive definite. The proof is non-perturbative and based on exact asymptotic behaviors of the vertex function imposed by Ward identities. Existence of an optimal $U$ for superconductivity is predicted. We also analyzed the pairing symmetry. In a large area of the parameter space of $J_{\rm A}$, $J_{\rm H}$, the ground state has a nematic $d$-wave singlet pairing, which, however, can lead to a $p$-wave-like nodal structure due to the Berry's phase on Fermi surfaces (or Euler obstruction).

cond-mat.supr-con↗