arXiv subjects

Debasish Banerjee

Publications and source records attributed to Debasish Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2024

Simulating optically-active spin defects with a quantum computer

There is a pressing need for more accurate computational simulations of the opto-electronic properties of defects in materials to aid in the development of quantum sensing platforms. In this work, we explore how quantum computers could be effectively utilized for this purpose. Specifically, we develop fault-tolerant quantum algorithms to simulate optically active defect states and their radiative emission rates. We employ quantum defect embedding theory to translate the Hamiltonian of a defect-containing supercell into a smaller, effective Hamiltonian that accounts for dielectric screening effects. Our approach integrates block-encoding of the dipole operator with quantum phase estimation to selectively sample the optically active excited states that exhibit the largest dipole transition amplitudes. We also provide estimates of the quantum resources required to simulate a negatively-charged boron vacancy in a hexagonal boron nitride cluster. We conclude by offering a forward-looking perspective on the potential of quantum computers to enhance quantum sensor capabilities and identify specific scenarios where quantum computing can resolve problems traditionally challenging for classical computers.

quant-ph↗

arXiv2024

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↗

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

Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories

In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free $U(1)$ quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is $H = \mathcal{O}_{\mathrm{kin}} + λ\mathcal{O}_{\mathrm{pot}}$, where $λ$ is a real-valued coupling, and $\mathcal{O}_{\mathrm{kin}}$ ($\mathcal{O}_{\mathrm{pot}}$) are summed local diagonal (off-diagonal) operators in the electric flux basis acting on the elementary plaquette $\square$. The spectrum of the model in its spin-$\frac{1}{2}$ representation on $L_x \times L_y$ lattices reveal the existence of sublattice scars, $|ψ_s \rangle$, which satisfy $\mathcal{O}_{\mathrm{pot},\square} |ψ_s\rangle = |ψ_s\rangle$ for all elementary plaquettes on one sublattice and $ \mathcal{O}_{\mathrm{pot},\square} | ψ_s \rangle =0 $ on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of $\mathcal{O}_{\mathrm{kin}}$. We demonstrate a ``triangle relation'' connecting the sublattice scars with nonzero integer eigenvalues of $ \mathcal{O}_{\mathrm{kin}} $ to particular sublattice scars with $\mathcal{O}_{\mathrm{kin}} = 0$ eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of $ \mathcal{O}_{\mathrm{kin}} $ become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another $U(1)$ quantum link model with a staggered short-ranged diagonal term.

hep-lat↗

arXiv2023

Temperature dependence of the static quark diffusion coefficient

The energy loss pattern of a low momentum heavy quark in a deconfined quark-gluon plasma can be understood in terms of a Langevin description. In thermal equilibrium, the motion can then be parametrized in terms of a single heavy quark momentum diffusion coefficient kappa, which needs to be determined nonperturbatively. In this work, we study the temperature dependence of kappa for a static quark in a gluonic plasma, with a particular emphasis on the temperature range of interest for heavy ion collision experiments.

hep-ph↗

arXiv2022

Achieving the quantum field theory limit in far-from-equilibrium quantum link models

Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work [Zache, Van Damme, Halimeh, Hauke, and Banerjee, at https://journals.aps.org/prd/abstract/10.1103/PhysRevD.106.L091502 has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of $1+1$D $\mathrm{U}(1)$ quantum link models approaches the quantum field theory limit already at small link spin length $S$. Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.

cond-mat.quant-gas↗

arXiv2022

Towards the continuum limit of a $(1+1)$d quantum link Schwinger model

The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for $U(1)$ gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-$S$ operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths $S$, large volume $N$, and vanishing lattice spacing $a$. By exactly solving Gauss' law for arbitrary $S$, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle $Θ=π$. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

hep-lat↗

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

Weak universality induced by $Q=\pm 2e$ charges at the deconfinement transition of a (2+1)-d $U(1)$ lattice gauge theory

Matter-free lattice gauge theories (LGTs) provide an ideal setting to understand confinement to deconfinement transitions at finite temperatures, which is typically due to the spontaneous breakdown (at large temperatures) of the centre symmetry associated with the gauge group. Close to the transition, the relevant degrees of freedom (Polyakov loop) transform under these centre symmetries, and the effective theory only depends on the Polyakov loop and its fluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified numerically, for the $U(1)$ LGT in $(2+1)$-d the transition is in the 2-d XY universality class, while for the $Z_2$ LGT, it is in the 2-d Ising universality class. We extend this classic scenario by adding higher charged matter fields, and show that the notion of universality is generalized such that the critical exponents $γ, ν$ can change continuously as a coupling is varied, while their ratio is fixed to the 2-d Ising value. While such weak universality is well-known for spin models, we demonstrate this for LGTs for the first time. Using an efficient cluster algorithm, we show that the finite temperature phase transition of the $U(1)$ quantum link LGT in the spin $S=\frac{1}{2}$ representation is in the 2-d XY universality class, as expected. On the addition of $Q = \pm 2e$ charges distributed thermally, we demonstrate the occurrence of weak universality.

hep-lat↗

arXiv2022

Crystalline phases at finite winding densities in a quantum link ladder

Condensed matter physics of gauge theories coupled to fermions can exhibit a rich phase structure, but are nevertheless very difficult to study in Monte Carlo simulations when they are afflicted by a sign problem. As an alternate approach, we use tensor network methods to explore the finite density physics of Abelian gauge theories without dynamical matter. As a concrete example, we consider the U(1) gauge invariant quantum link ladder with spin-1/2 gauge fields in an external electric field which cause the winding electric fluxes to condense in the ground state. We demonstrate how the electric flux tubes arrange themselves in the bulk giving rise to crystalline patterns, whose period can be controlled by tuning the external field. We propose observables to detect the transitions in ground state properties not only in numerical experiments, but also in future cold-atom realizations. A systematic procedure for reaching the thermodynamic limit, as well as extending the studies from ladders to extended geometries is outlined.

hep-lat↗

arXiv2022

Dynamical quantum phase transitions in spin-$S$ $\mathrm{U}(1)$ quantum link models

Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. With the strong ongoing experimental drive to quantum-simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin-$S$ $\mathrm{U}(1)$ quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of $S=1/2$ for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length $S>1/2$ this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the Wilson--Kogut--Susskind limit and its representation through the quantum link formalism.

cond-mat.str-el↗

arXiv2022

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a $\mathrm{U}(1)$ quantum link lattice gauge theory where the gauge fields, represented by spin-$\frac{1}{2}$ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d. This model allows us to smoothly tune between the $\mathrm{U}(1)$ quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

cond-mat.str-el↗

arXiv2022

Prominent quantum many-body scars in a truncated Schwinger model

The high level of control and precision achievable in current synthetic quantum matter setups has enabled first attempts at quantum-simulating various intriguing phenomena in condensed matter physics, including those probing thermalization or its absence in closed quantum systems. In a recent work [Desaules \textit{et al.} [arXiv:2203.08830], we have shown that quantum many-body scars -- special low-entropy eigenstates that weakly break ergodicity in nonintegrable systems -- arise in spin-$S$ quantum link models that converge to $(1+1)-$D lattice quantum electrodynamics (Schwinger model) in the Kogut--Susskind limit $S\to\infty$. In this work, we further demonstrate that quantum many-body scars exist in a truncated version of the Schwinger model, and are qualitatively more prominent than their counterparts in spin-$S$ quantum link models. We illustrate this by, among other things, performing a finite-$S$ scaling analysis that strongly suggests that scarring persists in the truncated Schwinger model in the limit $S\to\infty$. Although it does not asymptotically converge to the Schwinger model, the truncated formulation is relevant to synthetic quantum matter experiments, and also provides fundamental insight into the nature of quantum many-body scars, their connection to lattice gauge theories, and the thermalization dynamics of the latter. Our conclusions can be readily tested in current cold-atom setups.

cond-mat.quant-gas↗

arXiv2022

Weak Ergodicity Breaking in the Schwinger Model

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-$1/2$ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for $S>1/2$ since such theories converge to the lattice Schwinger model in the large-$S$ limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-$S$ $\mathrm{U}(1)$ quantum link models (QLMs) with staggered fermions. We find that QMBS persist at $S>1/2$, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-$S$ QLMs coupled to dynamical fermions.

cond-mat.str-el↗

arXiv2022

Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models

We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in $U(1)$ quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian $H=\mathcal{O}_{\mathrm{kin}} + λ\mathcal{O}_{\mathrm{pot}}$ where $\mathcal{O}_{\mathrm{pot}}$ ($\mathcal{O}_{\mathrm{kin}}$) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at $λ=0$ that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for $|λ| \lesssim \mathcal{O}(1)$ both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite $λ$ show a rich variety with those that are composed solely from the zero modes of $\mathcal{O}_{\mathrm{kin}}$, those that contain an admixture of both the zero and the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$, and finally those composed solely from the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$. We give analytic expressions for certain "lego scars" for the quantum dimer model on rectangular lattices where one of the linear dimensions can be made arbitrarily large, with the building blocks (legos) being composed of emergent singlets and other more complicated entangled structures.

cond-mat.str-el↗

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

Three-dimensional Gross-Neveu model with two flavors of staggered fermions

We introduce a strongly interacting lattice field theory model containing two flavors of massless staggered fermions with two kinds of interactions: (1) a lattice current-current interaction, and (2) an on-site four-fermion interaction. At weak couplings, we expect a massless fermion phase since our interactions become irrelevant at long distances. At strong couplings, based on previous studies, we argue that our lattice model contains two different massive fermion phases with different mechanisms of fermion mass generation. In one phase, fermions become massive through Spontaneous Symmetry Breaking (SSB) via the formation of a fermion bilinear condensate. In the other phase, fermion mass arises through a more exotic mechanism without the formation of any fermion bilinear condensate. Our lattice model is free of sign problems and can be studied using the fermion bag algorithm. The longer term goal here is to study both these mass generation phenomena in a single model and understand how different phases come together.

hep-lat↗

arXiv2021

Phases at finite winding number of an Abelian lattice gauge theory

Pure gauge theories are rather different from theories with pure scalar and fermionic matter, especially in terms of the nature of excitations. For example, in scalar and fermionic theories, one can create ultra-local excitations. For a gauge theory, such excitations need to be closed loops that do not violate gauge invariance. In this proceedings, we present a study on the condensation phenomenon associated with the string-like excitations of an Abelian lattice gauge theory. These phenomena are studied through numerical simulations of a $U(1)$ quantum link model in 2+1 dimensions in a ladder geometry using matrix product states. In this proceedings, we show the existence of ground states characterized by the presence of such string-like excitations. These are caused due to the condensation of torelons. We also study the relationship between the properties of the plaquettes in the ground state and the presence of such condensation phenomenon.

hep-lat↗