arXiv subjects

Emilie Huffman

Publications and source records attributed to Emilie Huffman.

At least 19 recordsLinked to original sources

arXiv2026

Spectral Fingerprints of Gauge Theories on a Quantum Computer

Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies. We show how it may be focused on any desired area of the spectrum in order to learn about the full \textit{fingerprint} of the model of interest: from its ground state phenomena such as quantum criticality, obtained from the lowest lying energies, to its thermalization behavior, obtained from the mid-spectrum. We demonstrate this technique specifically on a $(1+1)d$ non-Abelian $SO(3)$ gauge theory, providing a comprehensive analysis of the steps necessary for performing this algorithm, as well as what is possible in the near-term with superconducting quantum hardware, performing simulations with circuits that are $78$ two-qubit gates deep. We show how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method. Along the way, we propose a novel strategy for compiling the controlled-time evolutions needed for spectral sampling by means of Pauli-frame optimizations. We illustrate two physical applications of quantum spectral sampling -- disordered many-body transitions, and mid-spectrum densities of states -- and what postprocessing steps they require beyond the Fourier outputs of the algorithm.

quant-ph↗

arXiv2026

String dynamics of a (2+1)D U(1) quantum link model on a digital quantum computer

The (2+1)D U(1) pure gauge theory always exists in the confining phase, with strings of non-zero string tension giving a characteristic linear potential between static charges. This makes it a useful testing ground for quantum computing methods designed to study string dynamics of confining gauge theories. Here we implement a minimal U(1) quantum link model on a quantum computer with qubit degrees of freedom representing the dual height variables of the model. This facilitates an efficient realization of plaquette interactions and enables effective calculations of real-time dynamics that are inaccessible to traditional quantum Monte Carlo. A specifically tailored lattice geometry is chosen to match the heavy-hexagonal geometry of the IBM quantum hardware used here, minimizing non-adjacent qubit interactions. By performing quantum quenches from a simple initial string state, we probe the transverse quantum fluctuations of the string before it thermalizes. Our experimental results from digital quantum simulations, with up to 112 qubits, show good agreement with reference tensor-network calculations at short times and with thermal averages at long times. Near the phase transition, the quench dynamics exhibit large fluctuations of the initial string that extend across both spatial dimensions of the lattice. Nonetheless, our error-mitigated estimators from the quantum hardware also give accurate predictions in that regime, with noise-induced violations of local gauge symmetries comparable to finite-bond-dimension tensor-network results.

quant-ph↗

arXiv2026

Interplay of Gauss Law and the fermion sign problem in quantum link models with dynamical matter

Quantum Link Models with dynamical matter coupled to spin-$\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies $(G_e,G_o) = (d,\ -d)$, where $d$ is the spatial dimension and $e$ and $o$ are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.

hep-lat↗

arXiv2026

Generalizing Deconfined Criticality to 3D $N$-Flavor $\mathrm{SU}(2)$ Quantum Chromodynamics on the Fuzzy Sphere

The infra-red behaviour of gauge theories coupled to matter remains an open problem in quantum field theory. For a given gauge group, such theories are expected to flow to an interacting conformal fixed point over a range of fermion or scalar flavours, known as the `conformal window.' Their nature is important for understanding critical phases and phase transitions beyond the Landau paradigm like the deconfined quantum critical point (DQCP), yet remains challenging for conventional non-perturbative approaches. In this work, we study a family of fuzzy-sphere models corresponding to non-linear sigma models with $\mathrm{Sp}(N)$ global symmetry extended to the strongly-coupled region. These theories are expected have an infra-red fixed point described by $\mathrm{SU}(2)$ quantum chromodynamics (QCD) in three space-time dimensions with $N$ flavours of fermions. They can be viewed as a generalisation of the $\mathrm{SO}(5)$ DQCP, corresponding to $N=2$. We investigate them using quantum Monte Carlo for $N$ up to $16$. We find evidence that for $N\geq4$ the phase diagram contains a critical phase that appears to be absent for $N=2$. Within this phase, we measure the two-point correlation function and the excitation spectrum, which exhibit emergent conformal symmetry. We also extract the scaling dimension $\Delta_\phi$ of a leading operator and find consistency with large-$N$ expectations.

hep-th↗

arXiv2025

Sign-problem landscape of dimer, loop, and ground state sectors of a U(1) quantum link model

The fermion sign problem poses a formidable challenge to the use of Monte Carlo methods for lattice gauge theories with dynamical fermionic matter fields. A meron cluster algorithm recently formulated for gauge fields represented as spin-$\frac{1}{2}$ quantum links coupled to a single flavour of staggered fermions samples only two of the exponentially many Gauss law (GL) sectors at low temperatures, allowing the simulation of those two GL sectors at zero temperature in polynomial time. In this article, we analytically identify GL sectors which can be simulated without encountering the fermion sign problem in arbitrary spatial dimensions. Using large-scale exact diagonalization and cluster Monte Carlo methods, we explore the nature of phases in the GL sectors dominating at zero temperature. The ground state lives in a superselection sector free of the sign problem, and maps to the quantum dimer model with mobile monomers. The usual zero-charge GL sector suffers from the fermion sign problem, and maps to the fully packed loop model with mobile monomers. The role of the magnetic energy in causing transitions between GL sectors is outlined. We expect our results to be valid for truncated Kogut-Susskind gauge theories, beyond quantum link models.

hep-lat↗

arXiv2025

Geometric fragmentation and anomalous thermalization in cubic dimer model

While quantum statistical mechanics triumphs in explaining many equilibrium phenomena, there is an increasing focus on going beyond conventional scenarios of thermalization. Traditionally examples of non-thermalizing systems are either integrable, or disordered. Recently, examples of translationally-invariant physical systems have been discovered whose excited energies avoid thermalization either due to local constraints (whether exact or emergent), or due to higher-form symmetries. In this article, we extend these investigations for the case of 3D $U(1)$ quantum dimer models, which are lattice gauge theories with finite-dimensional local Hilbert spaces (also generically called quantum link models) with staggered charged static matter. Using a combination of analytical and numerical methods, we uncover a class of athermal states that arise in large winding sectors, when the system is subjected to external electric fields. The polarization of the dynamical fluxes in the direction of applied field traps excitations in 2D planes, while an interplay with the Gauss Law constraint in the perpendicular direction causes exotic athermal behaviour due to the emergence of new conserved quantities. This causes a geometric fragmentation of the system. We provide analytical arguments showing that the scaling of the number of fragments is exponential in the linear system size, leading to weak fragmentation. Further, we identify sectors which host fractonic excitations with severe mobility restrictions. The unitary evolution of fragments dominated by fractons is qualitatively different from the one dominated by non-fractonic excitations.

hep-lat↗

arXiv2024

Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in $(2+1)$-D

Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant subspace embedded onto local spin Hamiltonians for efficient quantum simulation. In $(1+1)d$ previous studies of the $SO(3)$ QLM coupled to adjoint fermionic matter have been shown to reflect key properties of QCD and nuclear physics, including distinct confining/deconfining phases and hadronic bound states. We extend the model to $(2+1)d$ dimensions for the first time, and report on our initial results. We review the construction of gauge-invariant state space for the proposed models, and study the single-plaquette ground state via exact-diagonalisation. We provide indications of a rich phase diagram which shows both spontaneous and explicit chiral symmetry breaking, confinement, and distinct magnetic phases characterised by different plaquette expectation values.

hep-lat↗

arXiv2024

Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms

The simulation of various properties of quantum field theories is rapidly becoming a testing ground for demonstrating the prowess of quantum algorithms. Some examples include the preparation of ground states, as well as the investigation of various simple wave packets relevant for scattering phenomena. In this paper, we study the ability of quantum algorithms to prepare ground states in a matter-free non-Abelian $SO(3)$ lattice gauge theory in $2+1$D in a phase where the global charge conjugation symmetry is spontaneously broken. This is challenging for two reasons: the necessity of dealing with a large Hilbert space for gauge theories compared to that of quantum spin models, and the closing of the gap between the two ground states, which becomes exponentially small as a function of the volume. To deal with the large Hilbert space of gauge fields, we demonstrate how the exact imposition of the non-Abelian Gauss Law in the rishon representation of the quantum link operator significantly reduces the degrees of freedom. Further, to resolve the gap, we introduce symmetry-guided ans\"{a}tze in the Gauss-Law-resolved basis for trial states as the starting point for the quantum algorithms to prepare the two lowest energy states. In addition to simulation results for a range of two-dimensional system sizes, we also provide experimental results from the trapped-ion-based quantum hardware, IonQ, when working on systems with four quantum links. The experimental/simulation results derived from our theoretical developments indicate the role of metrics--such as the energy and the infidelity--to assess the obtained results.

hep-lat↗

arXiv2023

Cluster-Algorithm-Amenable Models of Gauge Fields and Matter

Typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on cluster algorithms which do not involve the determinant and involve a more physically relevant sampling of the configuration space. We develop new cluster algorithms and design classes of models for fermions coupled to $\mathbb{Z}_2$ and $U(1)$ gauge fields that are amenable to being simulated by these cluster algorithms in a sign-problem free way. Such simulations should contain rich phase diagrams and are particularly relevant for quantum simulator experiments.

hep-lat↗

arXiv2023

Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional $SU(2)$ layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

cond-mat.str-el↗

arXiv2023

Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant

Ab-initio Monte Carlo simulations of strongly-interacting fermionic systems are plagued by the fermion sign problem, making the non-perturbative study of many interesting regimes of dense quantum matter, or of theories of odd numbers of fermion flavors, challenging. Moreover, typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on the meron cluster algorithm, which can solve the fermion sign problem in a class of models without involving the determinant. We develop and benchmark new meron algorithms to simulate fermions coupled to $\mathbb{Z}_2$ and $U(1)$ gauge fields in the presence of appropriate four-fermi interactions. Such algorithms can be used to uncover potential exotic properties of matter, particularly relevant for quantum simulator experiments. We demonstrate the emergence of the Gauss' Law at low temperatures for a $U(1)$ model in $(1+1)-$d.

hep-lat↗

arXiv2022

Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity

We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum Monte Carlo simulations. Importantly, interactions in our model are not only invariant under $\SU(2)$ symmetries of spin and charge like the Hubbard model, but they also preserve an Ising like electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either anti-ferromagnetism or superconductivity and that the transition at which both orders are simultaneously quantum critical, belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.

cond-mat.str-el↗

arXiv2022

Towards the real-time evolution of gauge-invariant $\mathbb{Z}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation

Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled lattice gauge theories. In this article, we benchmark the real-time dynamics of $\mathbb{Z}_2$ and $U(1)$ gauge invariant plaquette models using noisy intermediate scale quantum (NISQ) hardware, specifically the superconducting-qubit-based quantum IBM Q computers. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges. NISQ hardware suffers from significant decoherence and corresponding difficulty to interpret the results. We demonstrate the use of hardware-agnostic error mitigation techniques, such as circuit folding methods implemented via the Mitiq package, and show what they can achieve within the quantum volume restrictions for the hardware. Our study provides insight into the choice of Hamiltonians, construction of circuits, and the utility of error mitigation methods to devise large-scale quantum computation strategies for lattice gauge theories.

quant-ph↗

arXiv2022

Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization

The $3D$ Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the $2D$ Ising transition. Yet, the emergence of conformal invariance in the $3D$ Ising transition has rarely been explored directly, mainly due to unavoidable mathematical or conceptual obstructions. Here, we design an innovative way to study the quantum version of the $3D$ Ising phase transition on spherical geometry, using the "fuzzy (non-commutative) sphere" regularization. We accurately calculate and analyze the energy spectra at the transition, and explicitly demonstrate the state-operator correspondence (i.e. radial quantization), a fingerprint of conformal field theory. In particular, we have identified 13 parity-even primary operators within a high accuracy and 2 parity-odd operators that were not known before. Our result directly elucidates the emergent conformal symmetry of the $3D$ Ising transition, a conjecture made by Polyakov half a century ago. More importantly, our approach opens a new avenue for studying $3D$ CFTs by making use of the state-operator correspondence and spherical geometry.

cond-mat.stat-mech↗

arXiv2022

Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes

Quantum link models (QLMs) have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories (LGT), and are particularly suitable for realization on quantum simulators and computers. These models are known to host new phases of matter and act as a bridge between particle and condensed matter physics. In this article, we study the Abelian $U(1)$ lattice gauge theory in $(3+1)$-d tubes using large-scale exact diagonalization (ED). We are then able to motivate the phase diagram of the model with finite size scaling techniques (FSS), and in particular propose the existence of a Coulomb phase. Furthermore, we introduce the first models involving fermionic quantum links, which generalize the gauge degrees of freedom to be of fermionic nature. We prove that while the spectra remain identical between the bosonic and the fermionic versions of the $U(1)$-symmetric quantum link models in $(2+1)$-d, they are different in $(3+1)$-d. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.

hep-lat↗

arXiv2021

Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions

In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling $V$, we show that we can study the phase transition between the massless fermion phase at small-$V$ and a massive fermion phase at large-$V$. We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Numerical study shows that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling $U$. Here we obtain some critical exponents using lattices up to $L=48$.

hep-lat↗

arXiv2021

Introducing Fermionic Link Models

Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of $U(1)$ symmetric QLMs, both using a more conventional quantum spin-1/2 representation, as well as a fermionic representation. In 2D, we show that both bosonic and fermionic QLMs display the same physics. We then explore the models in 3D and find different behavior for the two QLMs. For the bosons, we see evidence for a quantum phase transition from a symmetry broken phase to a potential quantum spin liquid phase. For the fermions, we identify not one but two distinct phases in addition to a symmetry broken phase. We explore the symmetries of the ground state in the strong coupling limit, which breaks lattice symmetries and examine the spectrum for both models.

hep-lat↗

arXiv2020

Emergence of Gauss' Law in a $Z_2$ Lattice Gauge Theory

We explore a $Z_2$ Hamiltonian lattice gauge theory in one spatial dimension with a coupling $h$, without imposing any Gauss' law constraint. We show that in our model $h=0$ is a free deconfined quantum critical point containing massless fermions where all Gauss' law sectors are equivalent. The coupling $h$ is a relevant perturbation of this critical point and fermions become massive due to confinement and chiral symmetry breaking. To study the emergent Gauss' law sectors at low temperatures in this massive phase we use a quantum Monte Carlo method that samples configurations of the partition function written in a basis in which local conserved charges are diagonal. We find that two Gauss' law sectors, related by particle-hole symmetry, emerge naturally. When the system is doped with an extra particle, many more Gauss's law sectors related by translation invariance emerge. Using results in the range $0.01 < h \leq 0.15 $ we find that three different mass scales of the model behave like $h^{p}$ where $p \approx 0.579$.

cond-mat.str-el↗