arXiv subjects

Maine Christos

Publications and source records attributed to Maine Christos.

15 recordsLinked to original sources

arXiv2026

Non-Abelian Quantum Low-Density Parity Check Codes and Non-Clifford Operations from Gauging Logical Gates via Measurements

In this work, we introduce constructions for non-Abelian qLDPC codes obtained by gauging transversal Clifford gates using measurement and feedback. In particular, we identify two qualitatively different approaches to gauging qLDPC codes to obtain their non-Abelian counterparts. The first approach applies to codes that exhibit a generalized form of Poincar\'e duality and leads to a qLDPC non-Abelian Clifford stabilizer code, whose stabilizers are reminiscent of the action of a Type-III twisted quantum double. Our second approach applies to general qLDPC codes, and uses a graph of ancilla qubits which may be tailored to properties of the input codes to gauge a single transversal gate. For both constructions, the resulting gauged codes are shown to have properties analogous to 2D non-Abelian topological order -- e.g. the analog of a single anyon on a torus. We conclude by demonstrating that our gauging procedures enable magic state preparation via the measurement of logical Clifford gates. Consequently, our gauging constructions offer a protocol for performing non-Clifford operations on any qLDPC code.

quant-ph↗

arXiv2025

Fractionalized Fermi liquids and the cuprate phase diagram

We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$ at hole doping $p$, in contrast to the area $p/4$ in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla Layer Model (ALM). Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a $d$-wave superconductor via a Kosterlitz-Thouless transition of $h/(2e)$ vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. Increasing doping from the FL* phase in the ALM drives a transition to a conventional Fermi liquid (FL) at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.

cond-mat.str-el↗

arXiv2025

Thermal SU(2) lattice gauge theory for intertwined orders and hole pockets in the cuprates

The cuprate pseudogap phase displays Fermi arc spectral weight in photoemission and scanning tunneling microscopy (STM), while recent magnetotransport observations yield evidence for the existence of hole pockets of fractional area $p/8$, where $p$ is the doping density. We present a Monte Carlo study of a thermal SU(2) lattice gauge theory which can reconcile these observations. Our simulation includes the SU(2) gauge field $U$ of a $\pi$-flux spin liquid, and a SU(2) fundamental charge $e$ Higgs boson $B$. There is a Yukawa coupling between $B$, the fermionic spinons of the spin liquid, and the hole pockets of a fractionalized Fermi liquid. At the higher temperatures of the pseudogap, the finite-doping sign problem is evaded by including only thermal fluctuations of $B$ and $U$, while the fermions are diagonalized exactly for each boson background. Our study also yields a fractionalized description of intertwined orders at lower temperatures, including the onset of $d$-wave superconductivity by the expulsion of vortices with flux $h/(2e)$, each with charge-order halos. We discuss conditions under which quantum oscillations in the density of states from hole pockets of area $p/8$ could be observable in clean under-hole-doped cuprates.

cond-mat.str-el↗

arXiv2025

A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice

Early studies proposed a connection between cuprate superconductivity and fractionalized spin liquid states. But the low temperature phase diagram is dominated by states without fractionalization, with a competition between superconductivity and charge-ordered states which break translational symmetry. Our theory uncovers novel features associated with a particular spin-liquid presumed to underlie the pseudogap metal, and shows that it has multiple nearly-degenerate instabilities to confinement of fractionalized excitations, leading to antiferromagnetism, $d$-wave superconductivity, and/or charge order. Our theory provides routes to resolving a number of open puzzles on the cuprate phase diagram. The spin liquid is described by a SU(2) gauge theory of $N_f=2$ massless fundamental Dirac fermions, has an emergent SO(5)$_f$ global symmetry, and is presumed to confine at low energies to the Néel state. At non-zero doping (or smaller Hubbard repulsion at half-filling) we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges moving in $π$ flux. At half-filling, the low energy Higgs sector has $N_b=2$ relativistic bosons with a possible emergent SO(5)$_b$ global symmetry describing rotations between a $d$-wave superconductor, period-2 charge stripes, and the time-reversal breaking `$d$-density wave' state. We propose a deconfined quantum critical point between a confining state which breaks SO(5)$_f$ and a confining state which breaks SO(5)$_b$. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and $d$-wave superconductivity. A similar theory applies at non-zero doping and large $U$, with longer-range couplings of the chargons leading to charge order with longer periods.

cond-mat.str-el↗

arXiv2025

Quantum oscillations in the hole-doped cuprates and the confinement of spinons

A long standing problem in the study of the under-hole-doped cuprates has been the description of the Fermi surfaces underlying the high magnetic field quantum oscillations, and their connection to the higher temperature pseudogap metal. Harrison and Sebastian (arXiv:1103.4181) proposed that the pseudogap `Fermi arcs' are reconstructed into an electron pocket by field-induced charge density wave order. But computations on such a model (Zhang and Mei, arXiv:1411.2098) show an unobserved additional oscillation frequency from a Fermi surface arising from the backsides of the hole pockets completing the Fermi arcs. We describe a transition from a fractionalized Fermi liquid (FL*) model of the pseudogap metal, to a metal with bi-directional charge density wave order without fractionalization. We show that the confinement of the fermionic spinon excitations of the FL* across this transition can eliminate the unobserved oscillation frequency.

cond-mat.str-el↗

arXiv2025

Finite-momentum pairing and superlattice superconductivity in valley-imbalanced rhombohedral graphene

Inspired by the recent experimental discovery of superconductivity emerging from a time-reversal symmetry-breaking normal state in tetralayer rhombohedral graphene, we here investigate superconducting instabilities in this system. We classify the possible pairing instabilities, including states with commensurate and incommensurate center of mass momenta. As rotational symmetry is broken in the latter type of pairing states, their momentum-space structure is most naturally characterized by a 'valley-independent Chern number', measuring the relative chirality between the normal and superconducting state. We further demonstrate that superconductivity can condense at multiple incommensurate momenta simultaneously, leading to the spontaneous formation of a translational-symmetry-breaking superlattice superconductor. Studying multiple different pairing mechanisms and varying the degree of spin and valley polarization in the normal state, we compare the energetics of these superconductors. Our results demonstrate that valley-imbalanced rhombohedral tetralayer graphene can give rise to rich superconducting phenomenologies.

cond-mat.str-el↗

arXiv2024

Approximate symmetries, insulators, and superconductivity in continuum-model description of twisted WSe$_2$

Motivated by the recent discovery of superconductivity in twisted bilayer WSe$_2$, we analyze the correlated physics in this system in the framework of a continuum model for the moiré superlattice. Using the symmetries in a fine-tuned limit of the system, we identify the strong-coupling ground states and their fate when the perturbations caused by finite bandwidth, displacement field, and the phase of the intralayer potential are taken into account. We classify the superconducting instabilities and, employing a spin-fermion-like model, study the superconducting instabilities in proximity to these insulating particle-hole orders. This reveals that only a neighboring intervalley coherent phase (with zero or finite wave vector) is naturally consistent with the observed superconducting state. Depending on details, the superconductor will be nodal or a chiral gapped state while further including electron-phonon coupling leads to a fully gapped, time-reversal symmetric pairing state.

cond-mat.supr-con↗

arXiv2024

Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the $π$-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background $π$-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal $d$-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases which are very likely described by 2+1 dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional $d$-wave superconductor with gapless Bogoliubov quasiparticles at 4 nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semi-metal phases.

cond-mat.str-el↗

arXiv2023

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. For instance, recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of unusual consequences: most notably, the pairing invariant under all symmetries can have protected nodal lines or be fully gapped, depending on parameters, and the band-off-diagonal chiral d-wave state exhibits transitions between gapped and nodal regions upon varying the chemical potential. We demonstrate that nodal band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley-coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

cond-mat.supr-con↗

arXiv2023

Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor

We model the pseudogap state of the hole- and electron-doped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of long-range antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventional $d$-wave superconductivity by the condensation of a charge e Higgs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a background $\pi$-flux spin liquid. In all cases, we find that the $d$-wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electron-doped pseudogap metal with only electron pockets centered at wavevectors $(\pi, 0)$, $(0, \pi)$, and an electronic gap along the zone diagonals. Remarkably, in this case too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity.

cond-mat.str-el↗

arXiv2022

Critical metallic phase in the overdoped random $t$-$J$ model

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-$M$ limit with SU($M$) spin symmetry. The saddle point equations of this model are similar to appoximate dynamic mean field equations of realistic, non-random, $t$-$J$ models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparametrization symmetry, akin to SYK models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-$T$ resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase, and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

cond-mat.str-el↗

arXiv2021

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $ω_\ast \sim J q_{EA}$, and for $ω< ω_\ast$, the spectral density is linear in $ω$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $ω$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.

cond-mat.str-el↗

arXiv2021

Twistons in a Sea of Magic

Magic angle twisted trilayer graphene (TTG) has recently emerged as a new platform to engineer strongly correlated flat bands. Here, we reveal the structural and electronic properties of TTG using low temperature scanning tunneling microscopy at twist angles for which superconductivity has been observed. Real trilayer samples deviate from their idealized structure due to a strong reconstruction of the moiré lattice, which locks layers into near-magic angle, mirror symmetric domains comparable in size to the superconducting coherence length. The price for this magic relaxation is the introduction of an array of localized twist angle faults, termed twistons. These novel, gate-tunable moiré defects offer a natural explanation for the superconducting dome observed in transport and provide an avenue to probe superconducting pairing mechanisms through disorder tuning.

cond-mat.str-el↗

arXiv2021

Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene

Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions $ν$ of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of $ν$ and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutrality, $ν=0$, with additional spin-polarization being present at quarter ($ν=-2$) or three quarter ($ν=+2$) fillings of the quasi-flat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost flat bands and dispersive Dirac cones in twisted trilayer graphene.

cond-mat.str-el↗

arXiv2020

Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a "mechanism" for superconductivity. We present a comprehensive listing of plausible low-temperature orders, and the parent flavor symmetry breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis.

cond-mat.str-el↗