arXiv subjects

Philip W. Phillips

Publications and source records attributed to Philip W. Phillips.

At least 19 recordsLinked to original sources

arXiv2026

Transport and Temperature: Exact spectrum and Drude weight for the one-dimensional infinite-$U$ Hubbard model

Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, while exact analytical results for finite-temperature transport remain rare. Here, we investigate charge transport in the one-dimensional Hubbard model in the infinite-interaction limit. We first construct the exact \emph{and explicit - i.e. beyond Bethe ansatz} energy spectrum and eigenstates. Building on these explicit eigenstates, we derive a closed-form analytical expression for the charge Drude weight at arbitrary temperatures in the hole-dilute limit with a fixed number of doped holes, as well as analytical expressions in the low- and high-temperature limits at fixed hole density. We further show that, at low temperatures, the leading correction to the charge Drude weight is linear in $T$ when the number of holes is fixed, whereas it is quadratic in $T$ when the hole density is fixed. This analytically controlled example highlights the importance of identifying the underlying thermodynamic trajectory when interpreting finite-size numerical studies of charge transport in more general models.

cond-mat.str-el↗

arXiv2026

Green-function Zeros Encode Competing Mott and Charge-ordering Scales

While correlated insulators are devoid of low-energy quasiparticle poles, their Green functions retain clean momentum structure through zeros. However, precisely what zeros imply is not clear. By studying the extended Hubbard model both analytically and numerically, we establish a new paradigm for strongly correlated matter: the dispersion of Green function zeros is determined by both microscopic spin-spin correlations and defect kinematics. In fact, we find that the dispersion changes discontinuously across the transition between the Mott and the checkerboard charge-density wave phases as is expected for a first-order transition. This physics is robust to the inclusion of further neighbor hopping which simply fine tunes the spin-correlation or charge-defect kinematics. We conclude that it is the {\it dispersion} of the Green-function zeros that encode the physics of ordering resultant from the strong correlations.

cond-mat.str-el↗

arXiv2026

Local Current Algebra for the HK Universality Class

We show that a Hamiltonian in terms of the local real-space currents obeying an $\mathfrak{su}_1(2)$ affine Lie algebra eliminates the non-locality in the Hatsugai-Kohmoto model for a doped Mott insulator. We establish this local correspondence through the Bjorken-Johnson-Low prescription for anomalous commutators. With this result, we show that the charge susceptibility computed from the current Hamiltonian is identical to that with the elemental Fermionic fields. Consequently, the HK model is local in real space, though not in terms of the Fermionic fields, thereby eliminating the key criticism of this model and reinforcing the utility of current algebras for strong interactions.

cond-mat.str-el↗

arXiv2025

Proof that Momentum Mixing Hatsugai Kohmoto equals the Twisted Hubbard Model

We prove formally that the momentum-mixing Hatsugai-Kohmoto model (MMHK) is the Hubbard model with a twist. With this result in tow, we rely on the proof of Watanabe's that two models which differ by a twist must have the same bulk physics. Consequently, we have proven that MMHK=Hubbard in the charge sector.

cond-mat.str-el↗

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

Solving the SU($N$) Orbital Hatsugai-Kohmoto Model

We show that the physics of the SU($N$) Hubbard model can be realistically simulated with the recently developed orbital Hatsugai-Kohmoto model. In this approach, the momentum mixing absent from the band Hatsugai-Kohmoto model is included by grouping $n$-Hubbard atoms into a cluster. We take advantage of the rapid convergence of this scheme ($1/n^2$) and show that for $n\approx O(10)$, quantitative agreement with the determinantal quantum Monte Carlo method arises for the double occupancy as well as qualitative agreement for the filling and compressibility across the Mott transition. Additional features of this work are that we can obtain low-temperature physics, which could be qualitatively different from its high-temperature counterpart, and dynamical quantities without resorting to analytical continuation, thereby establishing the orbital Hatsugai-Kohmoto model as a useful alternative perspective for studying strong correlations in SU($N$) systems.

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↗

arXiv2025

Quantum Fisher Information Reveals UV-IR Mixing in the Strange Metal

The density-density response in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ has recently been shown to exhibit conformal symmetry. Using, the experimentally inferred conformal dynamic susceptibility, we compute the resultant quantum Fisher information (QFI), a witness to multi-partite entanglement. For a Fermi liquid, we find that the QFI grows quadratically as the temperature increases, consistent then with the phase space available for scattering in the standard theory of metals. By contrast, the QFI in a strange metal increases as a power law at as the temperature decreases, but ultimately extrapolates to a constant at $T=0$. The constant is of the form, $ω_g^{2Δ}$, where $Δ$ is the conformal dimension and $ω_g$ is the UV cutoff which is on the order of the pseudogap. As this constant {depends on both UV and IR properties}, it illustrates that multipartite entanglement in a strange metal exhibits UV-IR mixing, a benchmark feature of doped Mott insulators as exemplified by dynamical spectral weight transfer. We conclude with a discussion of the implication of our results for low-energy reductions of the Hubbard model.

cond-mat.str-el↗

arXiv2024

Conformally invariant charge fluctuations in a strange metal

The strange metal is a peculiar phase of matter in which the electron scattering rate, $τ^{-1} \sim k_B T/\hbar$, which determines the electrical resistance, is universal across a wide family of materials and determined only by fundamental constants. In 1989, theorists hypothesized that this universality would manifest as scale-invariant behavior in the dynamic charge susceptibility, $χ''(q,ω)$. Here, we present momentum-resolved inelastic electron scattering measurements of the strange metal Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ showing that the susceptibility has the scale-invariant form $χ''(q,ω) = T^{-ν} f(ω/T)$, with exponent $ν= 0.93$. We find the response is consistent with conformal invariance, meaning the dynamics may be thought of as occurring on a circle of radius $1/T$ in imaginary time, characterized by conformal dimension $Δ= 0.05$. Our study indicates that the strange metal is a universal phenomenon whose properties are not determined by microscopic properties of a particular material.

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

Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the "Hofstadter regime," where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo (DQMC) and density matrix renormalization group (DMRG) techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor $ν\leq 1$, bounded below by filling factor $ν= 1$ and bounded above by half-filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors $ν=1$ and $ν=3$. The phases near $ν=1$ are particle-hole asymmetric, and we observe a rapid decrease in ground state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands.

cond-mat.str-el↗

arXiv2024

The Smoke of Zaanen

Theoretical physics suffered a major loss with the death of my dear friend Jan Zaanen on January 18. This note is my remembrance of him.

physics.hist-ph↗

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

Nonlocal Conformal Field Theory

Using the recently developed notion of a fractional Virasoro algebra, we explore the implied operator product expansions in nonlocal conformal field theories and their geometric meaning. We probe the interplay between classical nonlocality in the functional-analytic sense and quantization in a two-dimensional setting and find that nonlocal quantum dynamics realize this fractional Virasoro algebra exclusively with a state dependent central charge. Notably, we prove that the widely studied free Gaussian fixed points with a fractional Laplacian kinetic term does not fit this criterion but that the RG flow associated non-Gaussian fixed points do.

hep-th↗

arXiv2023

Fifty years of Wilsonian renormalization and counting

Renormalization began as a tool to eliminate divergences in quantum electrodynamics but it is now the basis of our understanding of physics at different energy scales. I review its evolution with an eye towards physics beyond the Wilsonian paradigm.

cond-mat.stat-mech↗