# Judah Unmuth-Yockey's research while affiliated with Syracuse University and other places

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## Publications (66)

Motivated by the AdS/CFT correspondence, we use Monte Carlo simulation to investigate the Ising model formulated on tessellations of the two-dimensional hyperbolic disk. We focus in particular on the behavior of boundary-boundary correlators, which exhibit power-law scaling both below and above the bulk critical temperature indicating scale invaria...

Tensor network methods are becoming increasingly important for high-energy physics, condensed matter physics and quantum information science (QIS). We discuss the impact of tensor network methods on lattice field theory, quantum gravity and QIS in the context of High Energy Physics (HEP). These tools will target calculations for strongly interactin...

We discuss recent progress in Tensor Lattice Field Theory and economical, symmetry preserving, truncations suitable for quantum computations or simulations. We focus on spin and gauge models with continuous Abelian symmetries such as the Abelian Higgs model and emphasize noise-robust implementations of Gauss's law. We discuss recent progress concer...

Motivated by the AdS/CFT correspondence, we use Monte Carlo simulation to investigate the Ising model formulated on tessellations of the two-dimensional hyperbolic disk. We focus in particular on the behavior of boundary-boundary correlators, which exhibit power-law scaling both below and above the bulk critical temperature indicating scale invaria...

We propose a quantum algorithm to compute low-energy expectation values by sampling a partition function associated with the average energy. This sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates themselves. The observables calculated in this way are extrapolated from higher-energies to the ground state.

Certain aspects of some unitary quantum systems are well described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be accommodated in a corresponding unitary system + environment model via a generalization of Wigner-Weisskopf the...

The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group methods to study an effective three-dimensional $\mathbb{Z}_{3}$ model for the heavy-quark, high-temperature, stron...

The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model...

Motivated by recent attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we define an extended-O(2) model by adding a γcos(qφ) term to the ordinary O(2) model with angular values restricted to a 2π interval. In the γ→∞ limit, the model becomes an extended q-state clock model that reduces to t...

We study scalar fields propagating on Euclidean dynamical triangulations (EDTs). In this work, we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton’s gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding ener...

We study the emergence of de Sitter space in Euclidean dynamical triangulations (EDT). Working within the semi-classical approximation, it is possible to relate the lattice parameters entering the simulations to the partition function of Euclidean quantum gravity. We verify that the EDT geometries behave semiclassically, and by making contact with...

We define an extended-O(2) model by adding a $\gamma \cos(q\varphi)$ term to the ordinary O(2) model with angular values restricted to a $2\pi$ interval. In the $\gamma \rightarrow \infty$ limit, the model becomes an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuat...

We study the emergence of de Sitter space in Euclidean dynamical triangulations (EDT). Working within the semi-classical approximation, it is possible to relate the lattice parameters entering the simulations to the partition function of Euclidean quantum gravity. We verify that the EDT geometries behave semi-classically, and by making contact with...

We study scalar fields propagating on Euclidean dynamical triangulations (EDT). In this work we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton's gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy...

Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be accommodated in a corresponding unitary system + environment model via a generalization of Wigner-Weisskopf the...

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral fo...

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fie...

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyp...

We construct a tensor network representation of the partition function for the massless Schwinger model on a two-dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group we calculate the average plaquette and topolog...

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyp...

We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group (HOTRG) we calculate the phase diagram of the...

We study the SU(2) gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different observables between TRG and Monte Carlo simulations finding excellent agreement between the two methods. In practic...

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first order formalism in which the local frame and spin connection are treated as independent fie...

We discuss real-time evolution for the quantum Ising model in one spatial dimension with Ns sites. In the limit where the nearest-neighbor interactions J in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial states w...

We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and ultimately the gauge fields are integrated out, removing all initial gauge freedom. The resulting Hamiltonian can be...

We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different observables between TRG and Monte Carlo simulations finding excellent agreement between the two methods. In pract...

We discuss real time evolution for the quantum Ising model in one spatial dimension with $N_s$ sites. In the limit where the nearest neighbor interactions $J$ in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial sta...

We study Kähler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requiring vielbeins and spin connections. We work in the quenched approximation where the geometry is allowed to fluctuate but there is no backreaction from the matter on the...

We show that the Polyakov loop of the two-dimensional lattice Abelian Higgs model can be calculated using the tensor renormalization group approach. We check the accuracy of the results using standard Monte Carlo simulations and find good agreement. We show that the energy gap produced by the insertion of the Polyakov loop obeys universal finite-si...

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occ...

We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and the resulting Hamiltonian can be written as a rotor model. The energy eigenvalues for this Hamiltonian are computed...

We study K\"ahler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. We work in the quenched approximation where the geometry is allowed to fluctuate but there is no back-reaction from the matter on t...

We consider the four-dimensional Euclidean dynamical triangulations lattice model of quantum gravity based on triangulations of $S^{4}$. We couple it minimally to a scalar field in the quenched approximation. Our results suggest a multiplicative renormalization for the mass of the scalar field which is consistent with the shift symmetry of the disc...

A bstract
We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions be treated as Kähler-Dirac fields and the condensate arises from an anomaly associated with a U(1) gl...

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occ...

We show that the Polyakov loop of the two-dimensional lattice Abelian Higgs model can be calculated using the tensor renormalization group approach. We check the accuracy of the results using standard Monte Carlo simulations. We show that the energy gap produced by the insertion of the Polyakov loop obeys universal finite-size scaling which persist...

We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions be treated as K\"{a}hler-Dirac fields and the condensate arises from an anomaly associated with a $U(1)$ global...

We show that the gauged $O(2)$ spin model in 1+1 dimensions is a prime candidate for a first quantum simulation of a lattice gauge theory with optical lattices. Using a discrete tensor reformulation, we connect smoothly the space-time isotropic version used in most numerical simulations, to the continuous time limit corresponding to the Hamiltonian...

Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent attempts to use Renormalization Group (RG) ideas in the context of machine learning. We examine coarse graining procedures for perceptron models designed to identify the digits of the MNIST data. We discuss the correspondence be...

We calculate the von Neumann and R\'enyi bipartite entanglement entropy of the $O(2)$ model with a chemical potential on a 1+1 dimensional Euclidean lattice with open and periodic boundary conditions. We show that the Calabrese-Cardy conformal field theory predictions for the leading logarithmic scaling with the spatial size of these entropies are...

We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement ent...

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Renyi entanglement entropy S_2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state a...

We present a gauge-invariant effective action for the Abelian-Higgs model in
1+1 dimensions. It is constructed by integrating out the gauge field and then
using the hopping parameter expansion. The latter is tested with Monte Carlo
simulations for small values of the scalar self-coupling. In the opposite
limit, at infinitely large self-coupling, th...

We discuss the Tensor Renormalization Group (TRG) method for the O(2) model
with a chemical potential in 1+1 dimensions with emphasis on near
gapless/conformal situations. We emphasize the role played by the late Leo
Kadanoff in the development of this theoretical framework. We describe the
entanglement entropy in the superfluid phase (see arXiv:15...

We present a gauge-invariant effective action for the Abelian Higgs model
(scalar electrodynamics) with a chemical potential $\mu$ on a 1+1 dimensional
lattice. This formulation provides an expansion in the hopping parameter
$\kappa$ which we test with Monte Carlo simulations for a broad range of the
inverse gauge coupling $\beta_{pl}$ and small va...

We connect explicitly the classical O(2) model in 1 + 1 dimensions, a model sharing important features with U(1) lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional...

We present our progress on a study of the $O(3)$ model in two-dimensions
using the Tensor Renormalization Group method. We first construct the theory in
terms of tensors, and show how to construct $n$-point correlation functions. We
then give results for thermodynamic quantities at finite and infinite volume,
as well as 2-point correlation function...

The idea of blocking in configuration space has played an important role in
the development of the RG ideas. However, despite being half a century old and
having had a huge intellectual impact, generic numerical methods to perform
blocking for lattice models have progressed more slowly than sampling methods.
Blocking may be essential to deal with n...

We construct a sequence of steps connecting the classical $O(2)$ model in 1+1
dimensions, a model having common features with those considered in lattice
gauge theory, to physical models potentially implementable on optical lattices
and evolving at physical time. We show that the tensor renormalization group
formulation of the classical model allow...

We show that the Tensor Renormalization Group (TRG) method can be applied to
O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) and
SU(2)) on (hyper) cubic lattices. We explain that contrarily to some common
belief, it is very difficult to write compact formulas expressing the
blockspinning of lattice models. We show that i...

Using the example of the two-dimensional (2D) Ising model, we show that in
contrast to what can be done in configuration space, the tensor renormalization
group (TRG) formulation allows one to write exact, compact, and manifestly
local blocking formulas and exact coarse grained expressions for the partition
function. We argue that similar results s...

Fisher zeros are the zeros of the partition function in the complex
beta=2N_c/g^2 plane. When they pinch the real axis, finite size scaling allows
one to distinguish between first and second order transition and to estimate
exponents. On the other hand, a gap signals confinement and the method can be
used to explore the boundary of the conformal wi...

## Citations

... The dynamics of the Ising model in hyperbolic space are more interesting and less well understood than in flat space, but even the classical Ising model on H 2 is interesting [40][41][42]. ...

... In recent years, Hamiltonian-simulation methods based on tensor networks have significantly advanced [352][353][354], targeting generally low-dimensional theories and systems without volume-law entanglement. The progress in the applications of tensor networks to lattice gauge theories in both the Hamiltonian and path-integral formulations will continue over the next decade, as discussed in a Snowmass whitepaper [355] and recent reviews [356,357]. Nonetheless, more general Hamiltonian-simulation methods are needed, particularly pertinent to QCD and for real-time situations that exhibit an entanglement growth. ...

... For sufficiently large lattices, color singlet excitations will decay weakly down to stable states enabled by the near continuum of lepton states. In many ways, this resembles the quantum imaginarytime evolution (QITE) [184][185][186] algorithm, which is a special case of coupling to open systems, where quantum systems are driven into their ground state by embedding them in a larger system that acts as a heat reservoir. One can speculate that, in the future, quantum simulations of QCD will benefit from also including electroweak interactions as a mechanism to cool the strongly-interacting sector from particular classes of errors. ...

... While the perturbation considered here had an explicit Z N symmetry, which may have had a dominant effect on the resulting phase structure, it would also be interesting to explore the effect of perturbations with less symmetry to see how the results are modified. For example, N could be extended away from integer values as was considered in the limit of a large perturbation here [47,48]. Determining the effect of small perturbations with varying degrees of symmetry could be important to understanding the errors inherent in simulations on resource limited and noisy near-term quantum simulators. ...