arXiv subjects

Leyna Shackleton

Publications and source records attributed to Leyna Shackleton.

15 recordsLinked to original sources

arXiv2026

Unifying Dirac Spin Liquids on Square and Shastry-Sutherland Lattices via Fermionic Deconfined Criticality

We present a fermionic gauge theory for deconfined quantum criticality on the Shastry-Sutherland lattice and reveal its shared low-energy field-theoretic structure with the square lattice. Starting from an SU(2) $\pi$-flux parent state, we construct a continuum theory of Dirac spinons coupled to an SU(2) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux U(1) spin liquid and a gapless $\mathbb{Z}_{2}$ Dirac spin liquid. While the Shastry-Sutherland lattice permits additional symmetry-allowed fermion bilinears compared to the square lattice, the quantum field theories are identical up to additional irrelevant terms. Consequently, the Higgs potential structure and the leading low-energy theory coincide with the square-lattice case at the quantum critical point. The SO(5) critical point is expected to realize conformal deconfined criticality: we analyze it in a large flavor expansion, calculate its critical exponents, and identify the Yukawa coupling between the fermions and Higgs fields as the relevant perturbation that destabilizes it, consistent with pseudocritical behavior observed in recent Monte Carlo studies. We show that the emergent SO(5) order parameter acquires a large anomalous dimension at the critical point, leading to strongly enhanced N\'eel and VBS susceptibilities-a hallmark of fermionic deconfined quantum criticality consistent with numerical studies. Our results place recent numerical evidence for a gapless $\mathbb{Z}_{2}$ Dirac spin liquid on the Shastry-Sutherland lattice within a controlled field-theoretic framework and demonstrate that fermionic deconfined criticality on the square lattice-including critical exponents and stability-extends to frustrated lattices with reduced symmetry.

cond-mat.str-el↗

arXiv2025

Pathways from a chiral superconductor to a composite Fermi liquid

Recent experiments have reported chiral time-reversal broken superconductivity in $n$-layer rhombohedral graphene for $n = 4,5, 6$. Introducing a moir\'e potential by alignement with a hexagonal boron nitride substrate suppresses the superconductivity but leads instead to various fractional quantum anomalous Hall phenomena. Motivated by these observations, we consider the fate of the phase transition between (a chiral) Landau Fermi liquid (LFL) metal and a Composite Fermi Liquid (CFL) metal in the presence of attractive interactions. These are parent states, respectively, for the superconductor and the fractional quantum Hall states. For weak attractive interactions, the LFL is usually unstable to superconductivity while the CFL is stable. This raises the possibility of a direct continuous phase transition between the chiral superconductor and the CFL. However, we show that generically the LFL close to the transition to the CFL is stable against superconductivity. Thus the evolution between the CFL and chiral superconductor goes through an intermediate stable LFL phase for weak attractive interactions. With stronger interactions, the evolution can instead go through a non-Abelian paired quantum Hall state.

cond-mat.str-el↗

arXiv2025

Twisted quantum doubles are sign problem-free

The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be realized in a local sign problem-free Hamiltonian due to the non-positivity of the wavefunction. We show that this is not the case. Despite failing to be stoquastic - the standard criteria for the existence of a sign problem - the double semion model as well as all twisted quantum double phases of matter for finite groups $\mathcal{G}$ can be realized in local Hamiltonians that are sign problem-free within a stochastic series expansion. The lack of a sign problem is not fine-tuned and does not require the Hamiltonian to be exactly solvable, with sign problem-free perturbations allowing access to a variety of topological phase transitions.

cond-mat.str-el↗

arXiv2025

XDiag: Exact Diagonalization for Quantum Many-Body Systems

Exact diagonalization (ED) is a cornerstone technique in quantum many-body physics, enabling precise solutions to the Schr\"odinger equation for interacting quantum systems. Despite its utility in studying ground states, excited states, and dynamical behaviors, the exponential growth of the Hilbert space with system size presents significant computational challenges. We introduce XDiag, an open-source software package designed to combine advanced and efficient algorithms for ED with and without symmetry-adapted bases with user-friendly interfaces. Implemented in C++ for computational efficiency and wrapped in Julia for ease of use, XDiag provides a comprehensive toolkit for ED calculations. Key features of XDiag include the first publicly accessible implementation of sublattice coding algorithms for large-scale spin system diagonalizations, efficient Lin table algorithms for symmetry lookups, and random-hashing techniques for distributed memory parallelization. The library supports various Hilbert space types (e.g., spin-1/2, electron, and t-J models), facilitates symmetry-adapted block calculations, and automates symmetry considerations. The package is complemented by extensive documentation, a user guide, reproducible benchmarks demonstrating near-linear scaling on thousands of CPU cores, and over 20 examples covering ground-state calculations, spectral functions, time evolution, and thermal states. By integrating high-performance computing with accessible scripting capabilities, XDiag allows researchers to perform state-of-the-art ED simulations and explore quantum many-body phenomena with unprecedented flexibility and efficiency.

cond-mat.str-el↗

arXiv2024

Emergent polaronic correlations in doped spin liquids

The interplay between spin and charge degrees of freedom arising from doping a Mott insulating quantum spin liquid (QSL) has been a topic of research for several decades. Calculating properties of these fractionalized metallic states in single-band models are generally restricted to mean-field patron descriptions and small fluctuations around these states, which are insufficient for quantitative comparison of observables to measurements performed in strongly-correlated systems. In this work, we numerically study a class of correlated electronic wavefunctions which support fractionalized spin and charge excitations and which fully take into account gauge fluctuations through the enforcement of local Hilbert space constraints. By optimizing the energy of these wavefunctions against the hole-doped Fermi Hubbard Hamiltonian, we obtain a variational ansatz for describing the low-energy physics of this model. We compare measurements of hole-induced spin-spin correlation functions to measurements taken in low temperature cold-atom simulations of the Hubbard model and find quantitative agreement between the two. In particular, we demonstrate the emergence of magnetic polaron correlations in these metallic states.

cond-mat.str-el↗

arXiv2024

Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations

Disorder at the etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially-filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edge states in the graphene electrodes to measure electrical conductance and thermoelectric power across the GQD. We observe a rapid diminishing of electric conductance fluctuations and slowly decreasing thermoelectric power across the GQD with increasing temperature, consistent with recent theoretical predictions for the SYK regime.

cond-mat.mes-hall↗

arXiv2023

Sign-problem-free effective models of triangular lattice quantum antiferromagnets

The triangular lattice antiferromagnet with $S=1/2$ spins and nearest neighbor interactions is known to have long-range antiferromagnetic order, with nearest-neighbor spins at an angle of 120 degrees. Numerical studies of quantum phases proximate to this state have been limited to small systems because the of the sign-problem in Monte Carlo simulations in imaginary time. We propose an effective lattice model for quantum fluctuations of the antiferromagnetic order, and a sign-problem free Monte Carlo algorithm, enabling studies in large systems sizes. The model is a $\mathbb{Z}_2$ gauge theory coupled to gauge-charged scalars which have a relativistic dispersion in the continuum limit. Crucially, the gauge theory is odd, i.e. there is a static, background $\mathbb{Z}_2$ gauge charge on each site, accounting for the Berry phases of the half-odd-integer spins on each site. We present results of simulations on lattices of sizes up to $36 \times 36 \times 36$. Along with the antiferromagnetically ordered phase, our phase diagram has a valence bond solid state with a $\sqrt{12} \times \sqrt{12}$ unit cell, and a gapped $\mathbb{Z}_2$ spin liquid. Deconfined critical points or phases in intermediate regions are not ruled out by our present simulations.

cond-mat.str-el↗

arXiv2023

Conductance and thermopower fluctuations in interacting quantum dots

We model an interacting quantum dot of electrons by a Hamiltonian with random and all-to-all single particle hopping (of r.m.s. strength $t$) and two-particle interactions (of r.m.s. strength $J$). For $t \ll J$, such a model has a regime exhibiting the non-quasiparticle physics of the Sachdev-Ye-Kitaev model at temperatures $E_{\rm coh} \ll T \ll J$, and that of a renormalized Fermi liquid at $T \ll E_{\rm coh}$, where $E_{\rm coh} = t^2 / J$. Extending earlier work has computed the mean thermoelectric properties of such a dot weakly coupled to two external leads, we compute the sample-to-sample fluctuations in the conductance and thermopower of such a dot, and describe several distinct regimes. In all cases, the effect of the SYK interactions is to reduce the strength of the sample-to-sample fluctuations. We also find that in the regime where the mean transport co-efficients are determined only by the value of $J$ at leading order, the sample-to-sample fluctuations can be controlled by the influence of the smaller $t$.

cond-mat.str-el↗

arXiv2023

An exactly solvable dissipative spin liquid

Exactly solvable Hamiltonians with spin liquid ground states have proven to be extremely useful, not only because they unambiguously demonstrate that these phases can arise in systems of interacting spins but also as a pedagogical illustration of the concept and as a controlled starting point for further theoretical analysis. However, adding dissipative couplings to the environment - an important aspect for the realization of these phases - generically spoils the exact solvability. We here present and study a Lindbladian, describing a square-lattice spin-liquid with dissipative coupling to the environment, that admits an exact solution in terms of Majorana fermions coupled to static $\mathbb{Z}_2$ gauge fields. This solution allows us to characterize the steady-state solutions as well as ``quasiparticle'' excitations within the Lindbladian spectrum. This emergence of distinct types of quasiparticle excitations of the Lindbladian leads to a separation of timescales that govern the equilibration time of the expectation values of different classes of observables, some of which we identify as fractionalized string-like operators. This exactly solvable Lindbladian is expected to provide a starting point for a better understanding of the behavior of fractionalized systems under dissipative time evolution.

cond-mat.str-el↗

arXiv2022

Anisotropic deconfined criticality in Dirac spin liquids

We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless $\mathbb{Z}_2$ spin liquid. This $\mathbb{Z}_2$ spin liquid is of relevance to the spin $S=1/2$ square lattice antiferromagnet, where recent numerical studies have given evidence for such a phase existing in the regime of high frustration between nearest neighbor and next-nearest neighbor antiferromagnetic interactions (the $J_1$-$J_2$ model), appearing in a parameter regime between the vanishing of N\'eel order and the onset of valence bond solid ordering. The proximate Dirac spin liquid is unstable to monopole proliferation on the square lattice, ultimately leading to N\'eel or valence bond solid ordering. As such, we conjecture that this Higgs transition describes the critical theory separating the gapless $\mathbb{Z}_2$ spin liquid of the $J_1$-$J_2$ model from one of the two proximate ordered phases. The transition into the other ordered phase can be described in a unified manner via a transition into an unstable SU(2) spin liquid, which we have analyzed in prior work. By studying the deconfined critical theory separating the U(1) Dirac spin liquid from the gapless $\mathbb{Z}_2$ spin liquid in a $1/N_f$ expansion, with $N_f$ proportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponent $z \neq 1$. We analyze the consequences of this anisotropic dispersion by calculating the angular profiles of the equal-time N\'eel and valence bond solid correlation functions, and we find them to be distinct. We also note the influence of the anisotropy on the scaling dimension of monopoles.

cond-mat.str-el↗

arXiv2021

Deconfined criticality and a gapless $\mathbb{Z}_2$ spin liquid in the square lattice antiferromagnet

The theory for the vanishing of N\'eel order in the spin $S=1/2$ square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the $J_1$-$J_2$ model): a gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable $\mathbb{Z}_2$ spin liquid with massless Dirac spinon excitations; on the other side the critical point, the SU(2) spin liquid (the `$\pi$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant, and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless $\mathbb{Z}_2$ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z \neq 1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing $J_2/J_1$: N\'eel, gapless $\mathbb{Z}_2$ spin liquid, and valence bond solid.

cond-mat.str-el↗

arXiv2020

Quantum phase transition at non-zero doping in a random $t$-$J$ model

We present exact diagonalization results on finite clusters of a $t$-$J$ model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping $p=0$ extends to a metallic spin glass phase up to a transition $p=p_c \approx 1/3$. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near $p_c$. We also find signs of the phase transition in the entropy, entanglement entropy and compressibility, all of which exhibit a maximum near $p_c$. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for $p>p_c$, while this breaks down for $p<p_c$.

cond-mat.str-el↗

arXiv2020

Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models

In the study of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether $\mathcal{P}\mathcal{T}$-symmetry is spontaneously broken when eigenvalues meet. A particularly interesting set of eigenstates is provided by the degenerate ground-state subspace of systems with topological order. In this paper, we present simple criteria that guarantee the protection of $\mathcal{P}\mathcal{T}$-symmetry and, thus, the reality of the eigenvalues in topological many-body systems. We formulate these criteria in both geometric and algebraic form, and demonstrate them using the toric code and several different fracton models as examples. Our analysis reveals that $\mathcal{P}\mathcal{T}$-symmetry is robust against a remarkably large class of non-Hermitian perturbations in these models; this is particularly striking in the case of fracton models due to the exponentially large number of degenerate states.

cond-mat.str-el↗

arXiv2020

Spectral form factors of clean and random quantum Ising chains

We compute the spectral form factor of two integrable quantum-critical many body systems in one spatial dimension. The spectral form factor of the quantum Ising chain is periodic in time in the scaling limit described by a conformal field theory; we also compute corrections from lattice effects and deviation from criticality. Criticality in the random Ising chain is described by rare regions associated with a strong randomness fixed point, and these control the long time limit of the spectral form factor.

cond-mat.str-el↗

arXiv2019

Pinning of Diffusional Patterns by Non-Uniform Curvature

Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational symmetry. Deformations, e.g. by a bulge or indentation, break symmetry and can pin a pattern. We adapt methods of conformal mapping and perturbation theory to examine how curvature inhomogeneities select and pin patterns, and confirm the results numerically. The theory provides an analogy to quantum mechanics in a geometry-dependent potential and yields intuitive implications for cell membranes, tissues, thin films, and noise-induced quasipatterns.

cond-mat.soft↗