arXiv subjects

Philip Phillips

Publications and source records attributed to Philip Phillips.

At least 19 recordsLinked to original sources

arXiv2025

2D Helical Twist Controls Tricritical Point in an Interacting Majorana Chain

We analyze a series of interacting Majorana Fermion chains with finite range pair interactions with coupling strength $g$ that all exhibit a tri-critical point that separates an Ising critical phase from a supersymmetric gapped phase. We first notice that the interacting models exhibit an even-odd asymmetry depending on the number of sites, $\delta$, over which the interaction ranges. The even case exhibits competing order, thereby making it numerically untractable while the odd case exhibits an exactly solvable point at $g=-0.5$ where the entanglement entropy vanishes. By introducing a swirling geometrical twist, we map our 1D $\delta$-range chains to a series of 2D $\delta/2$-width models. Our new 2D models possess a unique helical boundary condition, constructed from 1D chains with the end of one connected to the start of another. We propose that the phase transition in the 1D system can be understood as a finite-system size transition in 2D. That is, the $g_c-\delta$ behavior is controlled by a 2D tri-critical universality class at $\delta\to\infty$ limit and is predicted by finite-size scaling theory.

cond-mat.str-el↗

arXiv2023

Consistency between reflection M-EELS and optical spectroscopy measurements of the long-wavelength density response of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$

The density fluctuation spectrum captures many fundamental properties of strange metals. Using momentum-resolved electron energy-loss spectroscopy (M-EELS), we recently showed that the density response of the strange metal Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) at large momentum, $q$, exhibits a constant-in-frequency continuum [Mitrano, PNAS $\textbf{115}$, 5392 (2018); Husain, PRX $\textbf{9}$, 041062 (2019)] reminiscent of the marginal Fermi liquid (MFL) hypothesis of the late 1980s [Varma, PRL $\textbf{63}$, 1996 (1989)]. However, reconciling this observation with infrared (IR) optics experiments, which show a well-defined plasmon excitation at $q \sim 0$, has been challenging. Here we report M-EELS measurements of Bi-2212 using 4$\times$ improved momentum resolution, allowing us to reach the optical limit. For momenta $q<0.04$ r.l.u., the M-EELS data show a plasmon feature that is quantitatively consistent with IR optics. For $q>0.04$ r.l.u., the spectra become incoherent with an MFL-like, constant-in-frequency form. We speculate that, at finite frequency, $\omega$, and nonzero $q$, some attribute of this Planckian metal randomizes the probe electron, causing it to lose information about its own momentum.

cond-mat.str-el↗

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 $\beta-$function in the presence of perturbing local interactions. In vicinity of the half-filled doped Mott state, the $\beta-$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↗

arXiv2021

Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene

In magic angle twisted bilayer graphene (MATBG), the moir\'e superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moir\'e and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here, using a scanning single-electron transistor microscope to measure local electronic compressibility, we simultaneously unveil novel sequences of broken-symmetry Chern insulators (CIs) and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations. Our measurements provide a complete experimental mapping of the energy spectrum and thermodynamic phase diagram of interacting Hofstadter subbands in MATBG. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels (zLLs) together with level crossings, indicating moir\'e valley splitting. We propose a unified flavor polarization mechanism to understand the intricate interplay of topology, interactions, and symmetry breaking as a function of density and applied magnetic field in this system.

cond-mat.str-el↗

arXiv2019

Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene

Recent experiments [arXiv: 1808.07865] on twisted bilayer graphene (TBLG) show that under hydrostatic pressure, an insulating state at quarter-filling of the moiré superlattice (i.e., one charge per supercell) emerges, in sharp contrast with the previous ambient pressure measurements of Cao et al. where the quarter--filling state (QFS) is a metal [Nature 556, 43 & 80 (2018)]. In fact, the insulating state at the other commensurate fillings of two and three charges per supercell is also enhanced under applied pressure. Based on realistic computations of the band structure for TBLG which show that the bandwidth first shrinks and then expands with increasing hydrostatic pressure, we compute the ratio of the potential to the kinetic energy, $r_s$. We find an experimentally relevant window of pressure for which $r_s$ crosses the threshold for a triangular Wigner crystal, thereby corroborating our previous work [Nano Lett. (2018)] that the insulating states in TBLG are due to Wigner rather than Mott physics. A key prediction of this work is that the window for the onset of the hierarchy of Wigner states that obtains at commensurate fillings is dome-shaped as a function of the applied pressure, which can be probed experimentally. Theoretically, we find a peak for crystallization around $1.5$ GPa relative to the experimental optimal pressure of $1.33$ GPa for the observation of the insulating states. Consequently, TBLG provides a new platform for the exploration of Wigner physics and its relationship with superconductivity.

cond-mat.str-el↗

arXiv2019

Anomalous Dimensions for Boundary Conserved Currents in Holography via the Caffarelli-Silvestri Mechanism for p-forms

Although it is well known that the Ward identities prohibit anomalous dimensions for conserved currents in local field theories, a claim from certain holographic models involving bulk dilaton couplings is that the gauge field associated with the boundary current can acquire an anomalous dimension. We resolve this conundrum by showing that all the bulk actions that produce anomalous dimensions for the conserved current generate non-local actions at the boundary. In particular, the Maxwell equations are fractional. To prove this, we generalize to p-forms the Caffarelli/Silvestre (CS) extension theorem. In the context of scalar fields, this theorem demonstrates that second-order elliptic differential equations in the upper half-plane in ${\mathbb R}_+^{n+1}$ reduce to one with the fractional Laplacian, $Δ^γ$, when one of the dimensions is eliminated. From the p-form generalization of the CS extension theorem, we show that at the boundary of the relevant holographic models, a fractional gauge theory emerges with equations of motion of the form, $Δ^γA^t= 0$ with $γ$ $\in R$ and $A^t$ the boundary components of the gauge field. The corresponding field strength $F = d_γA^t= dΔ^\frac{γ-1}{2} A^t$ is invariant under $A^t \rightarrow A^t+ d_γΛ$ with the fractional differential given by $d_γ\equiv (Δ)^\frac{γ-1}{2}d$, implying that $[A^t]=γ$ which is in general not unity.

hep-th↗

arXiv2018

Fractional Virasoro Algebras

We show that it is possible to construct a Virasoro algebra as a central extension of the fractional Witt algebra generated by non-local operators of the form, $L_n^a\equiv\left(\frac{\partial f}{\partial z}\right)^a$ where $a\in {\mathbb R}$. The Virasoro algebra is explicitly of the form, \beq [L^a_m,L_n^a]=A_{m,n}L^a_{m+n}+δ_{m,n}h(n)cZ^a \eeq where $c$ is the central charge (not necessarily a constant), $Z^a$ is in the center of the algebra and $h(n)$ obeys a recursion relation related to the coefficients $A_{m,n}$. In fact, we show that all central extensions which respect the special structure developed here which we term a multimodule Lie-Algebra, are of this form. This result provides a mathematical foundation for non-local conformal field theories, in particular recent proposals in condensed matter in which the current has an anomalous dimension.

hep-th↗

arXiv2017

Absence of a Charge Diffusion Pole at Finite Energies in an Exactly Solvable Interacting Flat Band Model in d-dimensions

Motivated by recent bounds for charge diffusion in critical matter, we investigate the question: What sets the scale for charge diffusion in a scale-invariant system? To make our statements precise, we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band regime. We find in this limit that the diffusion pole which would normally obtain at finite energy is pushed to zero energy resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale-invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, all be it, irrelevant to diffusion, which is the product of the squared band velocity and the density of states.

cond-mat.str-el↗

arXiv2017

Exact Form of Boundary Operators Dual to Interacting Bulk Scalar Fields in the AdS/CFT Correspondence

Using holographic renormalization coupled with the Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the precise form of the boundary operator dual to a bulk scalar field rather than just its average value. We show that even in the presence of interactions in the bulk, the boundary operator dual to a bulk scalar field is an anti-local operator, namely the fractional Laplacian. The propagator associated with such operators is of the general power-law (fixed by the dimension of the scalar field) type indicative of the absence of particle-like excitations at the Wilson-Fisher fixed point or the phenomenological unparticle construction. Holographic renormalization also allows us to show how radial quantization can be extended to such non-local conformal operators.

hep-th↗

arXiv2016

The effects of Coulomb interactions on the superconducting gaps in iron-based superconductors

Recent angle-resolved photoemission spectroscopy measurements of Co-doped LiFeAs report a large and robust superconducting gap on the $Γ$-centered hole band that lies 8 meV below the Fermi level. We show that, unlike a conventional superconductor described by BCS theory, a multiband system with strong interband Coulomb interactions can explain these observations. We model LiFeAs with a five-band model in which the shallow hole band is coupled with the other bands by only Coulomb interactions. Using Eliashberg theory, we find reasonable interaction parameters that reproduce the $T_c$ and all five gaps of LiFeAs. The energy independence of the Coulomb interactions then ensures the robustness of the gap induced on the shallow band. Furthermore, due to the repulsive nature of the Coulomb interactions, the gap changes sign between the shallow band and the other hole pockets, corresponding to an unconventional $s_{\pm}$ gap symmetry. Unlike other families of iron-based superconductors, the gap symmetry of LiFeAs has not been ascertained experimentally. The experimental implications of this sign-changing state are discussed.

cond-mat.supr-con↗

arXiv2015

Power-law Optical Conductivity from Unparticles: Application to the Cuprates

We calculate the optical conductivity using several models for unparticle or scale-invariant matter. Within a Gaussian action for unparticles that is gauged with Wilson lines, we find that the conductivity computed from the Kubo formalism with vertex corrections yields no non-trivial deviation from the free-theory result. This result obtains because at the Gaussian level, unparticles are just a superposition of particle fields and hence any transport property must be consistent with free theory. Beyond the Gaussian approach, we adopt the continuous mass formulation of unparticles and calculate the Drude conductivity directly. We show that unparticles in this context can be tailored to yield an algebraic conductivity that scales as $ω^{-2/3}$ with the associated phase angle between the imaginary and real parts of $\arctan\frac{σ_2}{σ_1}=60^\circ$ as is seen in the cuprates. Given the recent results\cite{Donos2014,Rangamani2015,Langley} that gravitational crystals lack a power-law optical conductivity, this constitutes the first consistent account of the $ω^{-2/3}$ conductivity and the phase angle seen in optimally doped cuprates. Our results indicate that at each frequency in the scaling regime, excitations on all energy scales contribute. Hence, incoherence is at the heart of the power-law in the optical conductivity in strongly correlated systems such as the cuprates.

cond-mat.str-el↗

arXiv2014

High-Energy Damping by Particle-Hole Excitations in the Spin-Wave Spectrum of Iron-Based Superconductors

Using a degenerate double-exchange model, we investigate the spin excitation spectra of iron pnictides. The model consists of local spin moments on each Fe site, as well as itinerant electrons from the degenerate $d_{xz}$ and $d_{yz}$ orbitals. The local moments interact with each other through antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg interactions, and they couple to the itinerant electrons through a ferromagnetic Hund coupling. We employ the fermionic spinon representation for the local moments and perform a generalized random-phase approximation calculation on both spinons and itinerant electrons. We find that in the $\left(π,0\right)$ magnetically-ordered state, the spin-wave excitation at $\left(π,π\right)$ is pushed to a higher energy due to the presence of itinerant electrons, which is consistent with a previous study using the Holstein-Primakoff transformation. In the paramagnetic state, the particle-hole continuum keeps the collective spin excitation near $\left(π,π\right)$ at a higher energy even without any $C_{4}$ symmetry breaking. The implications for recent high temperature neutron scattering measurements will be discussed.

cond-mat.str-el↗

arXiv2012

Towards the Standard Model of Fermi Arcs from a Wilsonian Reduction of the Hubbard Model

Two remarkable features emerge from the exact Wilsonian procedure for integrating out the high-energy scale in the Hubbard model. At low energies, the number of excitations that couple minimally to the electromagnetic gauge is less than the conserved charge, thereby implying a breakdown of Fermi liquid theory. In addition, two charge $e$ excitations emerge in the lower band, the standard projected electron and a composite entity (comprised of a hole and a charge $2e$ bosonic field) which give rise to poles and zeros of the single-particle Green function, respectively. The poles generate spectral weight along an arc centered at $(π/2,π/2)$ while the zeros kill the spectral intensity on the back-side of the arc. The result is the Fermi arc structure intrinsic to cuprate phenomenology. The presence of composite excitations also produces a broad incoherent pseudogap feature at the $(π,0)$ region of the Brillouin zone, thereby providing a mechanism for the nodal/anti-nodal dichotomy seen in the cuprates.

cond-mat.str-el↗

arXiv2011

Orbitally and Magnetically Induced Anisotropy in Iron-based Superconductors

Recent experimental developments in the iron pnictides have unambiguously demonstrated the existence of in-plane electronic anisotropy in the absence of the long-range magnetic order. Such anisotropy can arise from orbital ordering, which is described by an energy splitting between the two otherwise degenerate $d_{xz}$ and $d_{yz}$ orbitals. By including this phenomenological orbital order into a five-orbital Hubbard model, we obtain the mean-field solutions where the magnetic order is determined self-consistently. Despite sensitivity of the resulting states to the input parameters, we find that a weak orbital order that places the $d_{yz}$ orbital slightly higher in energy than the $d_{xz}$ orbital, combined with intermediate on-site interactions, produces band dispersions that are compatible with the photoemission results. In this regime, the stripe antiferromagnetic order is further stabilized and the resistivity displays the observed anisotropy. We also calculate the optical conductivity and show that it agrees with the temperature evolution of the anisotropy seen experimentally.

cond-mat.str-el↗

arXiv2011

Two distinct Mott-Insulator to Bose-glass transitions and breakdown of self averaging in the disordered Bose-Hubbard model

We investigate the instabilities of the Mott-insulating phase of the weakly disordered Bose-Hubbard model within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. We identify a new order parameter and associated correlation length scale that is capable of capturing the transition from a state with zero compressibility, the Mott insulator, to one in which the compressibility is finite, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. In the Mott insulator, the relative variance renormalizes to zero, whereas it diverges in the Bose glass. The divergence of the relative variance signals the breakdown of self-averaging. The length scale governing the breakdown of self-averaging is the distance between rare regions. This length scale is finite in the Bose glass but diverges at the transition to the Mott insulator with an exponent of $ν=1/D$ for incommensurate fillings. Likewise, the compressibility vanishes with an exponent of $γ=4/D-1$ at the transition. At commensurate fillings, the transition is controlled by a different fixed point at which both the disorder and interaction vertices are relevant.

cond-mat.dis-nn↗

arXiv2011

Vacancy Driven Orbital and Magnetic Order in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$

We investigate the effects of the $\sqrt{5}\times\sqrt{5}$ Fe vacancy ordering on the orbital and magnetic order in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$ using a three-orbital ($t_{2g}$) tight-binding Hamiltonian with generalized Hubbard interactions. We find that vacancy order enhances electron correlations, resulting in the onset of a block antiferromagnetic phase with large moments at smaller interaction strengths. In addition, vacancy ordering modulates the kinetic energy differently for the three $t_{2g}$ orbitals. This results in a breaking of the degeneracy between the $d_{xz}$ and $d_{yz}$ orbitals on each Fe site, and the onset of orbital order. Consequently, we obtain a novel inverse relation between orbital polarization and the magnetic moment. We predict that a transition from high-spin to low-spin states accompanied by a crossover from orbitally-disordered to orbitally-ordered states will be driven by doping the parent compound with electrons, which can be verified by neutron scattering and soft X-ray measurements.

cond-mat.str-el↗

arXiv2011

Universal features of Thermopower in High Tc systems and Quantum Criticality

In high Tc superconductors a wide ranging connection between the doping dependence of the transition temperature Tc and the room temperature thermopower Q has been observed. A "universal correlation" between these two quantities exists with the thermopower vanishing at optimum doping as noted by OCTHH (Obertelli, Cooper, Tallon, Honma and Hor). In this work we provide an interpretation of this OCTHH universality in terms of a possible underlying quantum critical point (QCP) at Tc. Central to our viewpoint is the recently noted Kelvin formula relating the thermopower to the density derivative of the entropy. Perspective on this formula is gained through a model calculation of the various Kubo formulas in an exactly solved 1-dimensional model with various limiting procedures of wave vector and frequency.

cond-mat.supr-con↗