arXiv subjects

Jinchao Zhao

Publications and source records attributed to Jinchao Zhao.

16 recordsLinked to original sources

arXiv2026

Quantum Geometric Friedel Oscillations

In conventional Friedel oscillations, the real-space charge density oscillations induced by an impurity are characterized by an oscillation period set by the Fermi momentum. In this work, we demonstrate that in metals with an isolated (nearly) flat band at the Fermi energy, quantum geometry induces a distinct type of oscillations, which we call the \emph{quantum geometric Friedel oscillations} (QGFOs). The period of the QGFOs is set by the momentum-space separation of the quantum metric hot spots of the isolated band. The conventional and quantum metric-induced oscillations can coexist at low temperatures. At higher temperatures, the conventional Friedel oscillation amplitudes away from the impurity site are set by the thermal length such that the oscillations can be easily washed out by temperature effects. Remarkably, the QGFOs decay length is set by the quantum metric length which is defined by the integration of the quantum metric of the isolated band. As a result, the QGFOs can persist even at temperatures much larger than the bandwidth of the isolated flat band. Moreover, the decay length is invariant for a wide range of temperature which is a striking result. In conclusion, we show that the quantum metric induces novel Friedel oscillations. Our work suggests that the measurement of the QGFOs is a powerful way to detect the quantum metric length (which is associated with the integral of the quantum metric) and the quantum metric hot spot separations (which are associated with the distribution of the quantum metric in the momentum space).

cond-mat.mes-hall↗

arXiv2026

Quantum Metric Localization and Quantum Metric Protection

The study of disorder effects in electronic systems is one of the central themes in physics. It is well established that in the Anderson localization regime, the localization length of electrons decreases monotonically as the disorder strength increases. Here, we demonstrate that the conventional Anderson localization paradigm fails completely in describing an isolated band with quantum metric, where the quantum metric of the band defines a length scale called the quantum metric length. For an isolated band with a finite bandwidth separated from other bands by a band gap $Δ$, weak disorder results in conventional Anderson localization behavior. However, as the disorder increases, the localization length ceases to decrease and becomes pinned at a value proportional to the quantum metric length, forming a localization length plateau. We term the regime within this localization length plateau as the quantum metric localization regime. Remarkably, the localization length does not deviate from the plateau until the disorder strength far exceeds $Δ$. We refer to this strong protection against disorder, characterized by the quantum metric length, as quantum metric protection. In this work, we first numerically demonstrate quantum metric localization using a 1D Lieb lattice. We then provide a simple physical picture based on the properties of Wannier functions to explain the origin of the localization length plateau. A supersymmetric field theory approach explains why the localization length is proportional to the quantum metric length and captures the crossover from Anderson localization to quantum metric localization. Our conclusions are broadly applicable to disordered electronic, photonic, and acoustic systems.

cond-mat.mes-hall↗

arXiv2026

Quantum Metric Bound State of Light

The spatial confinement of defect-induced bound states is conventionally governed by the effective mass in dispersive bands. More recently, Compact Localized States (CLSs) arising from exact destructive interference have been utilized to achieve confinement in flat bands. However, CLSs rely on pristine lattice symmetries and fine-tuned defect profiles. The introduction of a generic local impurity inevitably breaks these strict phase-matching conditions, resulting in extensive bound states whose fundamental length scale has remained an open question. Here, we establish a third regime of confinement: the quantum metric bound state. We provide a rigorous mathematical proof demonstrating that in the absence of kinetic energy and CLS protection, the exponential decay length of these states is lower-bounded by the quantum metric of the unperturbed flat band. We demonstrate the tightness of this geometric limit by constructing a family of highly tunable flat-band generators, and we verify its universality across diverse realistic architectures. Ultimately, this classification establishes the independently measurable quantum metric as a predictive design principle for engineering confined modes in synthetic wave platforms.

cond-mat.mes-hall↗

arXiv2026

Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark

While large language models (LLMs) with reasoning capabilities are progressing rapidly on high-school math competitions and coding, can they reason effectively through complex, open-ended challenges found in frontier physics research? And crucially, what kinds of reasoning tasks do physicists want LLMs to assist with? To address these questions, we present the CritPt (Complex Research using Integrated Thinking - Physics Test, pronounced "critical point"), the first benchmark designed to test LLMs on unpublished, research-level reasoning tasks that broadly covers modern physics research areas, including condensed matter, quantum physics, atomic, molecular & optical physics, astrophysics, high energy physics, mathematical physics, statistical physics, nuclear physics, nonlinear dynamics, fluid dynamics and biophysics. CritPt consists of 71 composite research challenges designed to simulate full-scale research projects at the entry level, which are also decomposed to 190 simpler checkpoint tasks for more fine-grained insights. All problems are newly created by 50+ active physics researchers based on their own research. Every problem is hand-curated to admit a guess-resistant and machine-verifiable answer and is evaluated by an automated grading pipeline heavily customized for advanced physics-specific output formats. We find that while current state-of-the-art LLMs show early promise on isolated checkpoints, they remain far from being able to reliably solve full research-scale challenges: the best average accuracy among base models is only 5.7%, achieved by GPT-5 (high), moderately rising to around 10% when equipped with coding tools. Through the realistic yet standardized evaluation offered by CritPt, we highlight a large disconnect between current model capabilities and realistic physics research demands, offering a foundation to guide the development of scientifically grounded AI tools.

cs.AI↗

arXiv2025

$\mathbb{Z}_2$ Universality of the Mott Transition

We demonstrate that the Mott transition exhibits universal scaling as a consequence of the breaking of a $\mathbb{Z}_2$ symmetry in momentum space. A direct consequence of this discrete symmetry breaking is the charge or Mott gap itself. From extensive numerics, we proffer that it is the charge compressibility that acts as the underlying order parameter as it is zero in the insulator and non-zero in the metallic state. Additionally, the Widom line (temperature of the extremum of the compressibility) obeys a universal scaling of $T_m=0.39U$ deep into the insulating state directly from $Z_2$ universality. Furthermore, the temperature at which the second derivative of the compressibility has a minimum is independent of lattice geometry, exhibiting a universal scaling of $|U-U_c|^α$ where $α\approx 1$. Finally, our computational approach reproduces the key features of the doping dependence of the compressibility demonstrated in recent cold-atom quantum simulators of the Hubbard model, thereby corroborating our conclusions on $\mathbb{Z}_2$ universality.

cond-mat.str-el↗

arXiv2025

Charge Susceptibility and Kubo Response in Hatsugai-Kohmoto-related Models

We study in depth the charge susceptibility for the band Hatsugai-Kohmoto (HK) and orbital (OHK) models. As either of these models describes a Mott insulator, the charge susceptibility takes on the form of a modified density response function with lower and upper Hubbard bands, thereby giving rise to a multi-pole structure. The particle-hole continuum consists of hot spots along the $ω$ vs $q$ axis arising from inter-band transitions. Such transitions, which are strongly suppressed in non-interacting systems, obtain here because of the non-rigidity of the Hubbard bands. This modified density response function gives rise to a plasmon dispersion that is inversely dependent on the momentum, resulting in an additional contribution to the conventional f-sum rule. This extra contribution originates from a long-range diamagnetic contribution to the current. This results in a non-commutativity of the long-wavelength ($q\rightarrow 0$) and thermodynamic ($L\rightarrow\infty$) limits. When the correct limits are taken, we find that the Kubo response computed with either open or periodic boundary conditions yields identical results that are consistent with the continuity equation contrary to recent claims. We also show that the long wavelength pathology of the current noted previously also plagues the Anderson impurity model interpretation of dynamical mean-field theory (DMFT).

cond-mat.str-el↗

arXiv2025

Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model

The Hubbard model is a standard theoretical tool for studying materials with strong electron-electron interactions, such as the cuprate superconductors. Unfortunately, interaction-driven phenomena such as the transition into the strongly correlated Mott insulator phase are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai-Kohmoto model displays similar Mott physics. Here we show how the Hatsugai-Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically re-introduce all the momentum mixing the original Hatsugai-Kohmoto model omits. This can be accomplished by grouping $n$-momenta into a cell and hybridizing them resulting in the momentum-mixing Hatsugai-Kohmoto (MMHK) model. We recover the Bethe ansatz ground state energy of the one-dimensional Hubbard model to within 1$\%$ from only ten mixed momenta. Overall the convergence scales as $1/n^2$ as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe the MMHK model offers an alternative tool for strongly correlated quantum matter.

cond-mat.str-el↗

arXiv2025

Incipient quantum spin Hall insulator under strong correlations

To assess prior mean-field claims that the interacting Kane-Mele model hosts a novel $z-$antiferromagnetic (AFM) Chern insulating phase for a wide range of sub-lattice potentials, we analyze the Kane-Mele-Hubbard model in the presence of a sub-lattice potential using non-perturbative determinant quantum Monte Carlo simulations. We find instead that the true low-temperature state is a quantum spin Hall insulator for intermediate values of the sub-lattice potential $λ_v$ and large on-site repulsion. Two kinds of magnetic fluctuations are found to compete: $z$- and $xy$-AFM. The latter dominates at low temperature leading to a stabilization of the quantum spin Hall state as opposed to $z-$AFM Chern insulator. Our work is consistent with the robust quantum spin Hall effects which are consistently observed at even-integer fillings over a wide range of parameters in twisted bilayer MoTe$_2$ and WSe$_2$ as well as AB stacked MoTe$_2$/WSe$_2$.

cond-mat.str-el↗

arXiv2025

The Luttinger Count is the Homotopy not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids

We show that the Luttinger-Ward functional can be formulated as an operator insertion in the path integral and hence can be thought of as a generalized symmetry. The key result is that the associated charge, always quantized, defines the homotopy, not the physical charge. The disconnect between the two arises from divergences in the functional or equivalently zeros of the single-particle Green function. Such divergences produce an anomaly of the triangle-diagram type. As a result of this anomaly, we are able to account for the various deviations\cite{rosch,dave,altshuler,osborne,l3,l5} of the Luttinger count from the particle density. As a consequence, non-Fermi liquids can be classified generally by the well known anomaly structures in particle physics. Charges descending from generalized symmetries, as in the divergence of the Luttinger-Ward functional, are inherently non-local, their key experimental signature.

cond-mat.str-el↗

arXiv2024

Dynamical Spectral Weight Transfer in the Orbital HK Model

We compute explicitly the low-energy spectral weight (LESW) in the lower Hubbard band using the orbital Hatsugai-Kohmoto (OHK) model. We show that the dynamical mixing enters the LESW with a universal slope independent of the number of orbitals. This independence on orbital number corroborates the rapid convergence of the OHK model to the Hubbard model. As a result, OHK is an effective simulator of Hubbard physics.

cond-mat.str-el↗

arXiv2024

Topological Phase Transition without Single-Particle-Gap Closing in Strongly Correlated Systems

We show here that numerous examples abound where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard non-interacting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does in fact close. These two gaps are the same in the non-interacting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

cond-mat.str-el↗

arXiv2023

1/4 is the new 1/2 when topology is intertwined with Mottness

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at $T=0$. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moire systems.

cond-mat.mes-hall↗

arXiv2023

Failure of Topological Invariants in Strongly Correlated Matter

We show exactly that standard `invariants' advocated to define topology for non-interacting systems deviate strongly from the Hall conductance whenever the excitation spectrum contains zeros of the single-particle Green function, $G$, as in general strongly correlated systems. Namely, we show that if the chemical potential sits atop the valence band, the `invariant' changes without even accessing the conduction band but by simply traversing the band of zeros that might lie between the two bands. Since such a process does not change the many-body ground state, the Hall conductance remains fixed. This disconnect with the Hall conductance arises from the replacement of the Hamiltonian, $h(\bb k)$, with $G^{-1}$ in the current operator, thereby laying plain why perturbative arguments fail.

cond-mat.str-el↗

arXiv2023

Proof of a Stable Fixed Point for Strongly Correlated Electron Matter

We establish the Hatsugai-Kohmoto model as a stable quartic fixed point (distinct from Wilson-Fisher) by computing the $β-$function in the presence of perturbing local interactions. In vicinity of the half-filled doped Mott state, the $β-$function vanishes for all local interactions regardless of their sign. The only flow away from the HK model is through the superconducting channel which lifts the spin degeneracy as does any ordering tendency. The superconducting instability is identical to that established previously\cite{nat1}. A corollary of this work is that Hubbard repulsive interactions flow into the HK stable fixed point in the vicinity of half-filling. Consequently, although the HK model has all-to-all interactions, nothing local destroys it. The consilience with Hubbard arises because both models break the $Z_2$ symmetry on a Fermi surface, the HK model being the simplest to do so. Indeed, the simplicity of the HK model belies its robustness and generality.

cond-mat.str-el↗

arXiv2022

Exact solution for finite center-of-mass momentum Cooper pairing

Pair density waves (PDWs) are superconducting states formed by ``Cooper pairs" of electrons containing a non-zero center-of-mass momentum. They are characterized by a spatially modulated order parameter and may occur in a variety of emerging quantum materials such as cuprates, transition metal dichalcogenides (TMDs) and Kagome metals. Despite extensive theoretical and numerical studies seeking PDWs in a variety of lattices and interacting settings, there is currently no generic and robust mechanism that favors a modulated solution of the superconducting order parameter in the presence of time reversal symmetry. Here, we study the problem of two electrons subject to an anisotropic ($d$-wave) attractive potential. We solve the two-body Schrodinger wave equation exactly to determine the pair binding energy as a function of the center-of-mass momentum. We find that a modulated (finite momentum) pair is favored over a homogeneous (zero momentum) solution above a critical interaction. Using this insight from the exact two-body solution, we construct a BCS-like variational many-body wave function and calculate the free energy and superconducting gap as a function of the center-of-mass momentum. A zero temperature analysis of the energy shows that the conclusions of the two-body problem are robust in the many-body limit. Our results lay the theoretical and microscopic foundation for the existence of PDWs.

cond-mat.supr-con↗

arXiv2022

Thermodynamics of an Exactly Solvable Model for Superconductivity in a Doped Mott Insulator

Computing superconducting properties starting from an exactly solvable model for a doped Mott insulator stands as a grand challenge. We have recently shown that this can be done starting from the Hatsugai-Kohmoto (HK) model which can be understood generally as the minimal model that breaks the non-local $\mathbb Z_2$ symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics [Phillips et al., Nature Physics 16, 1175 (2020); Huang et al., Nature Physics (2022)]. In the current work, we compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate $1/T_1$ and ultrasonic attenuation rate. Key differences arise with the standard BCS analysis from a Fermi liquid: 1) the free energy exhibits a local minimum at $T_p$ where the pairing gap turns on discontinuously above a critical value of the repulsive HK interaction, thereby indicating a first-order transition, 2) a tri-critical point emerges, thereby demarcating the boundary between the standard second-order superconducting transition and the novel first-order regime, 3) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy fuctional relative to that in BCS, 4) as this obtains in the strongly interacting regime, it is Mott physics that underlies the generic first-order transition, 5) the condensation energy exceeds that in BCS theory suggesting that multiple Mott bands might be a way of enhancing superconducting, 6) the heat-capacity jump is non-universal and increases with the Mott scale, 7) Mottness destroys the Hebel-Slichter peak in NMR, and 8) Mottness enhances the fall-off of the ultrasonic attenuation at the pairing temperature $T_p$. As several of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.

cond-mat.str-el↗