arXiv subjects

Shailesh Chandrasekharan

Publications and source records attributed to Shailesh Chandrasekharan.

At least 19 recordsLinked to original sources

arXiv2026

Continuum limit of a qubit-regularized SU(3) lattice gauge theory with glueballs

We show that a simple qubit-regularized $\mathrm{SU}(3)$ lattice gauge theory (LGT) on a plaquette chain admits a continuum limit with massive glueball excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the $\mathbb{Z}_3$ parafermion conformal field theory (CFT), which serves as the ultraviolet (UV) fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared (IR). The resulting relativistic massive particles can be interpreted as quasi one-dimensional analogues of glueballs. In the continuum theory we compute the ratio of the lowest glueball masses with opposite charge conjugation to be $m^{-}/m^{+} = \,1.459(2)$ and find $\sqrtσ/m^{+}\,= 0.2648(2)$, where $σ$ is the string tension between a static quark and antiquark.

hep-lat↗

arXiv2026

Confined and Deconfined Phases of Qubit Regularized Lattice Gauge Theories

We construct simple qubit-regularized Hamiltonian lattice gauge theories formulated in the monomer--dimer--tensor-network (MDTN) basis that are free of sign problems in the pure gauge sector. These models naturally realize both confined and deconfined phases. Using classical Monte Carlo methods, we investigate the associated finite-temperature phase transitions and show that they exhibit the expected universality classes of conventional SU(N) lattice gauge theories in various spacetime dimensions. Furthermore, we argue that second-order quantum phase transitions separating the confined and deconfined phases are likely to exist. Such critical points would provide a nonperturbative route to defining continuum limits of qubit-regularized gauge theories, potentially allowing Yang--Mills theory and related continuum gauge theories to emerge from finite-dimensional lattice constructions.

hep-lat↗

arXiv2026

Symmetric Mass Generation via Multicriticality in a 3D Lattice Gross-Neveu Model

We investigate a three-dimensional lattice model of two flavors of massless staggered fermions coupled through two independent four-fermion interactions, $U_I$ and $U_B$. Using large-scale fermion-bag Monte Carlo simulations, we map out the phase diagram in the $(U_I, U_B)$ parameter space and identify three distinct phases: a massless fermion phase, a symmetry-broken massive phase, and a symmetric massive phase. When one of the interactions is absent ($U_B=0$), the system undergoes a single continuous transition directly connecting the massless and symmetric massive phases, a feature previously associated with unconventional fermion mass generation. We find that turning on a nonzero $U_B$ separates this direct transition into two successive transitions with an intermediate symmetry-broken phase. The transition from the massless to the broken phase belongs to the Gross-Neveu universality class, while the transition from the broken to the symmetric massive phase falls into the three-dimensional XY universality class. Our results indicate that the special point at vanishing coupling, where the direct transition occurs, plays the role of a multicritical point organizing the surrounding phase structure. These findings provide a unified lattice perspective on conventional and unconventional mechanisms of fermion mass generation within a single model.

hep-lat↗

arXiv2026

Phase diagram of a lattice fermion model with symmetric mass generation

We study the phase structure of a model containing two flavors of massless staggered fermions interacting through two independent four-fermion couplings, UI and UB, formulated on a three-dimensional Euclidean space-time lattice. At UB = 0, this model is known to exhibit a direct second-order quantum phase transition between a massless fermion (MF) phase and a phase in which fermions acquire masses through the mechanism commonly referred to as symmetric mass generation (SMG). We demonstrate that introducing a small nonzero value of UB qualitatively alters this structure: the single exotic transition at UB = 0 splits into two distinct, conventional transitions, separated by an intermediate phase in which fermion masses arise through the standard mechanism of spontaneous symmetry breaking (SSB). The first of these is a Gross-Neveu transition separating the MF phase from the SSB-induced massive phase, while the second is a three-dimensional XY transition between the SSB phase and the SMG phase. Using the fermion-bag Monte Carlo method, we verify that the critical exponents associated with both transitions are consistent with the literature, thereby yielding a quantitative characterization of the resulting phase structure of the model.

hep-lat↗

arXiv2026

Asymptotic-freedom and massive glueballs in a qubit-regularized SU(2) gauge theory

We argue that a simple qubit-regularized $\mathrm{SU}(2)$ lattice gauge theory (LGT) on a plaquette chain serves as a pseudo-one-dimensional toy model for Yang-Mills (YM) theory in three spatial dimensions. We map the chain Hamiltonian to the Transverse Field Ising Model (TFIM) in a uniform magnetic field and demonstrate that it can be tuned to a continuum limit in which the short-distance physics is governed by the asymptotically free Ising conformal field theory (CFT) describing free Majorana fermions, while the long-distance regime contains massive excitations of the $E_8$ quantum field theory (QFT) that can be interpreted as one-dimensional analogues of glueballs. Furthermore, we find $\sqrtσ/m_1 = 0.249(1)$ where $σ$ is the string tension between two static quarks and $m_1$ is the mass of the lightest glueball.

hep-lat↗

arXiv2025

Symmetric mass generation as a multicritical point with enhanced symmetry

We explore the phase diagram of a lattice fermion model that exhibits three distinct phases: a massless fermion (MF) phase; a massive fermion phase with spontaneous symmetry breaking (SSB) induced by a fermion bilinear condensate; and a massive fermion phase with symmetric mass generation (SMG). Using the fermion-bag Monte Carlo method on large cubical lattices, we find evidence for traditional second-order critical points separating the first two and the latter two phases. Remarkably, these critical points appear to merge at a multicritical point with enhanced symmetry when the symmetry breaking parameter is tuned to zero, giving rise to the recently discovered direct second-order transition between the massless and symmetric massive fermion phases.

hep-lat↗

arXiv2025

Projected Density Matrix Sampling for Lattice Hamiltonians

Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for computing the low-lying spectrum of generic quantum Hamiltonians within a projection subspace. The method projects the thermal density matrix onto a subspace spanned by a chosen set of linearly independent states. It is free of Trotter discretization errors and systematically converges to the low-energy states which have finite overlap with the projection subspace as the $β$ parameter increases. While most effective for systems without a sign problem, the method also yields information about low-energy spectra when sign problems are present. We illustrate the approach on two problems. For the sign-free case, we compute the first four low-energy levels in the scaling limit of the one-dimensional Ising model with both transverse and longitudinal fields, demonstrating the flow from the conformal limit to the massive $E_8$ quantum field theory. For the sign-problem case, we apply the method to the frustrated Shastry-Sutherland model and benchmark it against exact diagonalization on small lattices. We also present results for larger systems beyond the lattice sizes accessible to exact diagonalization, while limited to small $β$ where sign problems occur. Our method provides a general route toward quantum Monte Carlo spectroscopy for lattice Hamiltonians.

cond-mat.str-el↗

arXiv2025

Qubit Regularization of Quantum Field Theories

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.

hep-lat↗

arXiv2025

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Traditional $\mathrm{SU}(N)$ lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) $V_λ$ of the $\mathrm{SU}(N)$ gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps $\{λ_\ell\}$ and monomer tensors on sites labeled by $\{λ_s\}$. These tensors naturally define a local site Hilbert space, $\mathcal{H}^g_s$, on which gauge transformations act. Gauss's law introduces an additional index $α_s = 1, 2, \dots, \mathcal{D}(\mathcal{H}_s^g)$ that labels an orthonormal basis of the gauge-invariant subspace of $\mathcal{H}^g_s$. This monomer-dimer tensor-network (MDTN) basis, $\left| \{λ_s\},\{λ_\ell\},\{α_s\}\right\rangle$, of the physical Hilbert space enables the construction of new qubit-regularized $\mathrm{SU}(N)$ gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ gauge theory in $d=2$ and $d=3$ spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in $d=1$, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

hep-lat↗

arXiv2025

Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization

We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition. This is achieved by lowering the fugacity of Fock-vacuum sites in the loop-gas configuration space to zero in the thermodynamic limit. Some of the universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional XY model. Our model is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time and helps understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning.

hep-lat↗

arXiv2024

Transverse Field $γ$-Matrix Spin Chains

We introduce a simple lattice spin model that is written in terms of the well-known four-dimensional $γ$-matrix representation of the Clifford algebra. The local spins with a four-dimensional Hilbert space transform in a spinorial $(1/2,0) \oplus (0,1/2)$ representation of $SO(4)$, a symmetry of our model. When studied on a chain, and as a function of a transverse field tuning parameter, our model undergoes a quantum phase transition from a valence bond solid phase to a critical phase that is described by an $SU(2)_1$ WZW field theory.

cond-mat.str-el↗

arXiv2024

Worldline Monte Carlo method for few body nuclear physics

In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $\exp(-βH)$ where $H$ is the lattice Hamiltonian and $β$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $β$ which are not very large. Computing these bound state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective field theory and show how it would work in the one and two body sectors.

nucl-th↗

arXiv2024

A qubit regularization of asymptotic freedom without fine-tuning

Other than the commonly used Wilson's regularization of quantum field theories (QFTs), there is a growing interest in regularizations that explore lattice models with a strictly finite local Hilbert space, in anticipation of the upcoming era of quantum simulations of QFTs. A notable example is Euclidean qubit regularization, which provides a natural way to recover continuum QFTs that emerge via infrared fixed points of lattice theories. Can such regularizations also capture the physics of ultraviolet fixed points? We present a novel regularization of the asymptotically free massive continuum QFT that emerges at the Berezenski-Kosterlitz-Thouless (BKT) transition through a hard core loop-gas model, discussing the advantages this model provides compared to traditional regularizations. In particular, we demonstrate that without the need for fine-tuning, it can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition.

hep-lat↗

arXiv2023

Phases of 2d massless QCD with qubit regularization

We investigate the possibility of reproducing the continuum physics of 2d SU(N) gauge theory coupled to a single flavor of massless Dirac fermions using qubit regularization. The continuum theory is described by N free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR). In this work, we explore how well these features can be reproduced using the Kogut-Susskind Hamiltonian with a finite-dimensional link Hilbert space and a generalized Hubbard coupling. Using strong coupling expansions, we show that our model exhibits a gapped dimer phase and another phase described by a spin-chain. Furthermore, for N=2, using tensor network methods, we show that there is a second-order phase transition between these two phases. The critical theory at the transition can be understood as an SU(2)_1 WZW model, using which we determine the phase diagram of our model quantitatively. Using the confinement properties of the model we argue how the UV physics of free fermions could also emerge, but may require further modifications to our model.

hep-lat↗

arXiv2023

Topological terms with qubit regularization and relativistic quantum circuits

Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models with rich phase diagrams. Some of the phases can contain topological terms which lead to critical phases. In this work we introduce and study the SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue that qubit models in this regularization scheme contain several phases including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) at long distances, and two massive phases one of which is trvially gapped and the other which breaks the lattice translation symmetry. We construct a simple space-time Euclidean lattice model with a single coupling U and study it using the Monte Carlo method. We show the model has a critical phase at small U and a trivially massive phase at large U with a first order transition separating the two. Another feature of our model is that it is symmetric under space-time rotations, which means the temporal and spatial lattice spacing are connected to each other. The unitary time evolution operator obtained by a Wick rotation of the transfer matrix of our model can help us compute the physics of the k = 1 WZW CFT in real time without the need for tuning the temporal lattice spacing to zero. We use this idea to introduce the concept of a relativistic quantum circuit on a discrete space-time lattice.

hep-lat↗

arXiv2023

Vacuum Entanglement Harvesting in the Ising Model

The low-energy states of quantum many body systems, such as spin chains, are entangled. Using tensor network computations, we demonstrate a protocol that distills Bell pairs out of the ground state of the prototypical transverse-field Ising model. We explore the behavior of rate of entanglement distillation in various phases, and possible optimizations of the protocol. Finally, we comment on the protocol as we approach quantum criticality defining a continuum field theory.

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

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

hep-lat↗