arXiv subjects

Andrew Millis

Publications and source records attributed to Andrew Millis.

At least 19 recordsLinked to original sources

arXiv2026

Large scale neural quantum states reveal the interplay between superconductivity and quantum criticality in the Hofstadter-Hubbard model

Understanding how a parent insulating state shapes the superconductivity that emerges upon doping is a long-standing problem dating back to Anderson's resonating-valence-bond proposal. The triangular-lattice Hofstadter-Hubbard model with $\pi/2$ flux per plaquette offers an ideal setting: at half filling it hosts two distinct parent states---an integer quantum Hall insulator and a chiral spin liquid---separated by a topological phase transition. Using neural quantum states on tori of up to $432$ sites, we present strong evidence that the transition is continuous, with a vanishing $2e$ charge gap and critical charge fluctuations. Upon doping, we find a topological superconductor on either side of the transition. While the pairing order parameter remains nearly unchanged across the transition, the superfluid stiffness is strongly enhanced near the critical point. The energy scale of the superconductor is therefore set not by which parent state is doped, but by proximity to the transition between them. Our results establish neural quantum states as a powerful tool for understanding the interplay between unconventional electronic correlations and superconductivity.

cond-mat.str-el↗

arXiv2026

Plasmon dynamics in graphene

Plasmon are collective oscillations of mobile electrons with dynamics controlled by their charge stiffness("Drude weight"). Using terahertz spacetime metrology, we probe Plasmon dynamics of mono- and bi-layer graphene. In both systems, the experimentally measured Drude weight systematically exceeds the prediction based on non-interacting electronic system. The relative enhancement increases as the carrier density decreases. We attribute the observed deviation to the interplay of interactions and wave function structure of the Dirac fermions in multi-layer graphene. Our results establish that pseudospin structure of the single-particle electronic wave function can directly influence collective excitations, with implications that extend beyond graphene to a broad class of quantum materials.

cond-mat.mes-hall↗

arXiv2025

Superconductivity in Electron Liquids: Precision Many-Body Treatment of Coulomb Interaction

More than a century after discovery, the theory of conventional superconductivity remains incomplete. While the importance of electron-phonon coupling is understood, a controlled first-principles treatment of Coulomb interaction is lacking. Current ab initio calculations of superconductivity rely on a phenomenological downfolding approximation, replacing Coulomb interaction with a repulsive pseudopotential \mu*, and leaving ambiguities in electron-phonon coupling with dynamical Coulomb interactions unresolved. We address this via an effective field theory approach, integrating out high-energy electronic degrees of freedom using variational Diagrammatic Monte Carlo. Applied to the uniform electron gas, this establishes a microscopic procedure to implement downfolding, define the pseudopotential, and express dynamical Coulomb effects on electron-phonon coupling via the electron vertex function. We find the bare pseudopotential significantly larger than conventional values. This yields improved pseudopotential estimates in simple metals and tests density functional perturbation theory accuracy for effective electron-phonon coupling. We present an ab initio workflow computing superconducting Tc from the anomalous vertex's precursory Cooper flow. This infers Tc from normal state calculations, enabling reliable estimates of very low Tc (including near quantum phase transitions) beyond conventional reach. Validating our approach on simple metals without empirical tuning, we resolve long-standing discrepancies and predict a pressure-induced transition in Al from superconducting to non-superconducting above ~60GPa. We propose ambient-pressure Mg and Na are proximal to a similar critical point. Our work establishes a controlled ab initio framework for electron-phonon superconductivity beyond the weak-correlation limit, paving the way for reliable Tc calculations and novel material design.

cond-mat.supr-con↗

arXiv2025

Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model

We investigate the weak interaction integer quantum Hall (IQH) phase, the intermediate interaction phase identified as a chiral spin liquid (CSL) and the transition between them in the triangular lattice Hofstadter-Hubbard model at a density of one electron per site in an orbital magnetic field corresponding to one-quarter flux per plaquette. Our primary tool is the finite system density matrix renormalization group (DMRG) method with both interaction-strength scan and fixed interaction techniques for cylinders of circumference 3, 5, and 7 and lengths up to 240. For the IQH phase, we use single particle exact diagonalization to clarify finite size effects, including an excess charge on the edges of our cylinders, and the limitations of entanglement spectra degeneracies on small circumference cylinders. For both phases, we use DMRG to study the entanglement spectra, the entanglement entropy, and the effect of flux insertion on charge and spin pumping, all of which show key differences between the two phases. To study the transition, we use interaction-strength scans extending between the two phases, and apply a scaling data collapse of a bond-dimerization order parameter to extract critical exponents. We also extract critical behavior from the divergence of correlation lengths on the IQH side, measuring decay away from edges of both the dimerization order parameter and transverse edge currents. The critical behavior and exponents are consistent with an Ising transition in 1+1 dimensions. Finally, we obtain excited states in various quantum number sectors finding that the gap to a charge neutral momentum $\pi$ excitation corresponding to fluctuations of the dimerization order parameter closes in the vicinity of the critical point but gaps to other excitations remain large.

cond-mat.str-el↗

arXiv2025

Electron-Phonon Coupling in Correlated Metals: A Dynamical Mean-Field Theory Study

Strong electron-electron interactions are known to significantly modify the electron-phonon coupling relative to the predictions of density functional theory, but this effect is challenging to calculate with realistic theories of strongly correlated materials. Here we define and calculate a version of the EPC applicable beyond band theory by combining first principles density functional theory plus dynamical mean-field theory with finite difference phonon perturbations, presenting results for several representative phonon modes in two materials of interest. In the three-orbital correlated metal SrVO$_3$, we find that intra-V-$t_{2g}$ band correlation significantly increases the coupling of these electrons to a Jahn-Teller phonon mode that splits the degenerate orbital energies, while slightly reducing the coupling associated with a breathing phonon that couples to the charge on each V atom. In the infinite layer cuprate CaCuO$_2$, we find that local correlation within the $d_{x^2-y^2}$ orbital derived band has a modest effect on coupling of near-Fermi surface electrons to optical breathing modes. In both cases, the interaction correction to the electron-phonon coupling predicted by dynamical mean-field theory has a significant dependence on the electronic frequency, arising from a lattice-distortion dependence of the correlated electron dynamics, showing the inadequacy of the simple picture in which correlations change static local susceptibilities. We also show that the electron-phonon scattering and phonon lifetimes associated with these phonon modes are modified by the electronic correlation. Our findings shed light on the material- and mode-specific role of dynamical electronic correlation in electron-phonon coupling and highlight the importance of developing efficient computational methods for treating electron-phonon coupling in correlated materials.

cond-mat.str-el↗

arXiv2025

Elastocaloric signature of the excitonic instability in Ta$_2$NiSe$_5$

On cooling through a temperature $T_S$ of around 324 K, Ta$_2$NiSe$_5$ undergoes a transition from a semimetallic state to one with a gapped electronic spectrum which is suspected to be an excitonic insulator. However, at this transition the structure also changes, from orthorhombic to monoclinic, leaving open the question of whether it is driven primarily by excitonic ordering or by a lattice instability. A lattice instability of this symmetry would correspond to softening of a B$_{2g}$ optical or acoustic phonon mode. Here, we report that elastocaloric measurements of Ta$_2$NiSe$_5$ with induced B$_{2g}$ strain reveal a thermodynamic susceptibility described by a Curie-Weiss law with a Curie temperature $T^*$ of 298 K. The fact that $T^*$ is close to $T_S$ rules out the possibility that the B$_{2g}$ acoustic mode is responsible for the transition. Since prior Raman measurements have shown minimal softening of the B$_{2g}$ optical mode as well, our finding strengthens the case that the transition is largely excitonic in nature. Our work underscores the potential of using strain as a tool for separating electronic and lattice contributions in phase transitions.

cond-mat.str-el↗

arXiv2024

Spinon pairing induced by chiral in-plane exchange and the stabilization of odd-spin Chern number spin liquid in twisted ${\rm MoTe}_2$

The unusual structure and symmetry of low-energy states in twisted transition metal dichalcogenides leads to large in-plane spin-exchange interactions between spin-valley locked holes. We demonstrate that this exchange interaction can stabilize a gapped spin-liquid phase with a quantized spin-Chern number of three when the twist angle is sufficiently small and the system lies in a Mott insulating phase. The gapped spin liquid may be understood as arising from spinon pairing in the DIII Altland-Zirnbauer symmetry class. Applying an out of plane electric field or increasing the twist angle is shown to drive a transition respectively to an anomalous Hall insulator or an in-plane antiferromagnet. Recent experiments indicate that a spin-Chern number three phase occurs in twisted MoTe$_2$ at small twist angles with a transition to a quantum anomalous Hall phase as the twist angle is increased above a critical value of about $2.5^\circ$ in absence of applied electric field.

cond-mat.str-el↗

arXiv2024

Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model

Recent advances in moir\'e engineering motivate the study of lattice models of strongly-correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120$^\circ$ antiferromagnetic phases. We use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.

cond-mat.str-el↗

arXiv2024

Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles

Many of the important phases observed in twisted transition metal dichalcogenide homobilayers are driven by short-range interactions, which should be captured by a local tight binding description since no Wannier obstruction exists for these systems. Yet, published theoretical descriptions have been mutually inconsistent, with honeycomb lattice tight binding models adopted for some twist angles, triangular lattice models adopted for others, and with tight binding models forsaken in favor of band projected continuum models in many numerical simulations. Here, we derive and study a minimal model containing both honeycomb orbitals and a triangular site that represents the band physics across a wide range of twist angles. The model provides a natural basis to study the interplay of interaction and topology in these heterostructures. It elucidates from generic features of the bilayer the sequence of Chern numbers occurring as twist angle is varied, and the microscopic origin of the magic angle at which flat-band physics occurs. At integer filling, the model successfully captures the Chern ferromagnetic and van-Hove driven antiferromagnetic insulators experimentally observed for small and large angles, respectively, and allows a straightforward calculation of the magneto-electric properties of the system.

cond-mat.str-el↗

arXiv2023

Two-Dimensional Moir\'e Polaronic Electron Crystals

Two-dimensional moir\'e materials have emerged as the most versatile platforms for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in WSe2/WS2 moir\'e superlattices. We find that ultrafast electronic excitation leads to melting of the Mott states on time scales five times longer than predictions from the charge hopping integrals and the melting rates are thermally activated, with activation energies of 18 and 13 meV for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. DFT calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16 meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moir\'e interfaces.

cond-mat.str-el↗

arXiv2023

Topological superconductivity in doped magnetic moir\'e semiconductors

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moir\'e band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tuanble strength, which may be large. Together with the low moir\'e carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.

cond-mat.supr-con↗

arXiv2023

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2023

Mott insulators with boundary zeros

The topological classification of electronic band structures is based on symmetry properties of Bloch eigenstates of single-particle Hamiltonians. In parallel, topological field theory has opened the doors to the formulation and characterization of non-trivial phases of matter driven by strong electron-electron interaction. Even though important examples of topological Mott insulators have been constructed, the relevance of the underlying non-interacting band topology to the physics of the Mott phase has remained unexplored. Here, we show that the momentum structure of the Green's function zeros defining the ``Luttinger surface" provides a topological characterization of the Mott phase related, in the simplest description, to the one of the single-particle electronic dispersion. Considerations on the zeros lead to the prediction of new phenomena: a topological Mott insulator with an inverted gap for the bulk zeros must possess gapless zeros at the boundary, which behave as a form of ``topological antimatter'' annihilating conventional edge states. Placing band and Mott topological insulators in contact produces distinctive observable signatures at the interface, revealing the otherwise spectroscopically elusive Green's function zeros.

cond-mat.str-el↗

arXiv2022

Chiral Kondo Lattice in Doped MoTe$_2$/WSe$_2$ Bilayers

We theoretically study the interplay between magnetism and a heavy Fermi liquid in the AB stacked transition metal dichalcogenide bilayer system MoTe$_2$/WSe$_2$ in the regime in which the Mo layer supports localized magnetic moments coupled by interlayer electron tunnelling to a weakly correlated band of itinerant electrons in the W layer. We show that the interlayer electron transfer leads to a chiral Kondo exchange, with consequences including a strong dependence of the Kondo temperature on carrier concentration, a topological hybridization gap and an anomalous Hall effect. The theoretical model exhibits two phases, a small Fermi surface magnet and a large Fermi surface heavy Fermi liquid; the transition between them is first order. A low-energy theory is developed for the the transport properties of the two states. Implications of our results for present and future experiments on MoTe$_2$/WSe$_2$ bilayer heterostructures are discussed.

cond-mat.str-el↗

arXiv2022

Tunable Stripe Order and Weak Superconductivity in the Moir\'e Hubbard Model

The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases, which, upon doping exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole binding energy is found to be highly tunable revealing an experimentally accessible regime where holes become attractive. In this attractive regime, we study the superconducting correlation function and point out the possibility of weak superconductivity.

cond-mat.str-el↗

arXiv2022

Dynamical Mean Field Studies of Infinite Layer Nickelates: Physics Results and Methodological Implications

This article summarizes recent work on the many-body (beyond density functional theory) electronic structure of layered rare-earth nickelates, both in the context of the materials themselves and in comparison to the high-temperature superconducting (high-$T_c$) layered copper-oxide compounds. It aims to outline the current state of our understanding of layered nickelates and to show how the analysis of these fascinating materials can shed light on fundamental questions in modern electronic structure theory. A prime focus is determining how the interacting physics defined over a wide energy range can be estimated and "downfolded" into a low energy theory that would describe the relevant degrees of freedom on the $\sim 0.5$ eV scale and that could be solved to determine superconducting and spin and charge density wave phase boundaries, temperature-dependent resistivities, and dynamical susceptibilities.

cond-mat.str-el↗

arXiv2020

Polarity dependent heating at the phase interface in metal-insulator transitions

Current-driven insulator-metal transitions are in many cases driven by Joule heating proportional to the square of the applied current. Recent nano-imaging experiments in Ca$_2$RuO$_4$ reveal a metal-insulator phase boundary that depends on the direction of an applied current, suggesting an important non-heating effect. Motivated by these results, we study the effects of an electric current in a system containing interfaces between metallic and insulating phases. Derivation of a heat balance equation from general macroscopic Onsager transport theory, reveals a heating term proportional to the product of the current across the interface and the discontinuity in the Seebeck coefficient, so that heat can either be generated or removed at an interface, depending on the direction of the current relative to the change in material properties. For parameters appropriate to Ca$_2$RuO$_4$, this heating can be comparable to or larger than Joule heating. A simplified model of the relevant experimental geometry is shown to provide results consistent with the experiments. Extension of the results to other inhomogeneous metal-insulator transition systems is discussed.

cond-mat.str-el↗

arXiv2020

Electromagnetic coupling in tight-binding models for strongly correlated light and matter

We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations, because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multi-center Power-Zienau-Woolley transformation yields a dipolar Hamiltonian which incorporates the light-matter coupling via both Peierls phases and a polarization density. We compare this dipolar gauge Hamiltonian and the straightforward Coulomb gauge Hamiltonian for a one-dimensional solid, to describe sub-cycle light-driven electronic motion in the semiclassical limit, and a coupling of the solid to a quantized cavity mode which renormalizes the band-structure into electron-polariton bands. Both descriptions yield the same result when many bands are taken into account, but the dipolar Hamiltonian is more accurate when the model is restricted to few electronic bands, while the Coulomb Hamiltonian requires fewer electromagnetic modes.

cond-mat.str-el↗