arXiv subjects

Arnab Sen

Publications and source records attributed to Arnab Sen.

At least 37 records · Page 2Linked to original sources

arXiv2024

Observation of sequential three-body dissociation of camphor molecule -- a native frame approach

The three-body dissociation dynamics of the dicationic camphor molecule (C$_{10}$H$_{16}$O$^{2+}$) resulting from Auger decay are investigated using soft X-ray synchrotron radiation. A photoelectron-photoion-photoion coincidence (PEPIPICO) method, a combination of a velocity map imaging (VMI) spectrometer and a time-of-flight (ToF) spectrometer is employed to measure the 3D momenta of ions detected in coincidence. The ion mass spectra and the ion-ion coincidence map at photon energies of 287.9 eV (below the C 1s ionization potential) and 292.4 eV (above the C 1s ionization potential for skeletal carbon) reveal that fragmentation depends on the final dicationic state rather than the initial excitation. Using the native frame method, three new fragmentation channels are discussed; (1) CH$_2$CO$^+$ + C$_7$H$_{11}^+$ + CH$_3$, (2) CH$_3^+$ + C$_7$H$_{11}^+$ + CH$_2$CO, and (3) C$_2$H$_5^+$ + C$_6$H$_9^+$ + CH$_2$CO. The dominating nature of sequential decay with deferred charge separation is clearly evidenced in all three channels. The results are discussed based on the experimental angular distributions and momenta distributions, corroborated by geometry optimization of the ground, monocationic, and dicationic camphor molecule.

physics.chem-ph↗

arXiv2024

Central Limit Theorem in Disordered Monomer-Dimer Model

We consider the disordered monomer-dimer model on general finite graphs with bounded degrees. Under the finite fourth moment assumption on the weight distributions, we prove a Gaussian central limit theorem for the free energy of the associated Gibbs measure with a rate of convergence. The central limit theorem continues to hold under a nearly optimal finite $(2+ε)$-moment assumption on the weight distributions if the underlying graphs are further assumed to have a uniformly subexponential volume growth. This generalizes a recent result by Dey and Krishnan (arXiv:2109.12716) who showed a Gaussian central limit theorem in the disordered monomer-dimer model on cylinder graphs. Our proof relies on the idea that the disordered monomer-dimer model exhibits a decay of correlation with high probability. We also establish a central limit theorem for the Gibbs average of the number of dimers where the underlying graph has subexponential volume growth and the edge weights are Gaussians.

math.PR↗

arXiv2024

Scaling limit of soliton lengths in a multicolor box-ball system

The box-ball systems are integrable cellular automata whose long-time behavior is characterized by soliton solutions, with rich connections to other integrable systems such as the Korteweg-de Vries equation. In this paper, we consider a multicolor box-ball system with two types of random initial configurations and obtain sharp scaling limits of the soliton lengths as the system size tends to infinity. We obtain a sharp scaling limit of soliton lengths that turns out to be more delicate than that in the single color case established in [Levine, Lyu, Pike '20]. A large part of our analysis is devoted to studying the associated carrier process, which is a multi-dimensional Markov chain on the orthant, whose excursions and running maxima are closely related to soliton lengths. We establish the sharp scaling of its ruin probabilities, Skorokhod decomposition, strong law of large numbers, and weak diffusive scaling limit to a semimartingale reflecting Brownian motion with explicit parameters. We also establish and utilize complementary descriptions of the soliton lengths and numbers in terms of modified Greene-Kleitman invariants for the box-ball systems and associated circular exclusion processes.

math.PR↗

arXiv2024

Minimal spanning arborescence

We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient trees, the infinite volume limit exists almost surely. We also prove that for nonamenable, unimodular graphs, the limit is almost surely one-ended assuming a certain sufficient condition that guarantees the existence of the limit. This object cannot be studied using well-known algorithms, such as Kruskal's or Prim's algorithm, to sample the minimal spanning tree which has been instrumental in getting analogous results about them (Lyons, Peres, and Schramm). Instead, we use a recursive algorithm due to Chu, Liu, Edmonds, and Bock, which leads to a novel stochastic process which we call the \emph{loop contracting random walk}. This is similar to the well-known and widely studied loop erased random walk, except instead of erasing loops we contract them. The full algorithm bears similarities with the celebrated Wilson's algorithm to generate uniform spanning trees and can be seen as a certain limit of the original Wilson's algorithm.

math.PR↗

arXiv2024

Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z$, $β$, $γ$ and $ν$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to $1$, implying that the critical point is governed by a conformal field theory. The values obtained for $β/ν$, $γ/ν$, and $ν$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h \gg 1$ or $h \ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

cond-mat.stat-mech↗

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

Free energy of a diluted spin glass model with quadratic Hamiltonian

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our results in particular provide the first example of the diluted Shcherbina-Tirozzi model, whose limiting free energy can be derived at any inverse temperature and external field.

math.PR↗

arXiv2023

Limiting eigenvalue distribution of heavy-tailed Toeplitz matrices

We consider an $N \times N$ random symmetric Toeplitz matrix with an i.i.d. input sequence drawn from a distribution that lies in the domain of attraction of an $α$-stable law for $0 < α< 2$. We show that under an appropriate scaling, its empirical eigenvalue distribution, as $N \to \infty$, converges weakly to a random symmetric probability distribution on $\mathbb{R}$, which can be described as the expected spectral measure of a certain random unbounded self-adjoint operator on $\ell^2(\mathbb{Z})$. The limiting distribution turns out to be almost surely subgaussian. Furthermore, the support of the limiting distribution is bounded almost surely if $0<α<1$ and is unbounded almost surely if $1\leq α<2$.

math.PR↗

arXiv2023

Strong Hilbert space fragmentation via emergent quantum drums in two dimensions

We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as ``quantum drums''. These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed ``wire'' and a ``junction of two wires'' respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.

cond-mat.stat-mech↗

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

Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

$^{87}{\rm Rb}$ atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf r}$ and ${\bf r'}$. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $Δ$ and $λ$ respectively. We show that when $V_{\bf r r'} \gg(\ll) Δ, λ$ for $|{\bf r}-{\bf r'}|=1(>1)$, these ladders host a plateau for a wide range of $λ/Δ$ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density $1/4$. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning $λ_c/Δ=1/3$ which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{{\bf r} {\bf r'}} = V_0 /|{\bf r}-{\bf r'}|^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $λ_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.

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↗

arXiv2021

Periodically driven Rydberg chains with staggered detuning

We study the stroboscopic dynamics of a periodically driven finite Rydberg chain with staggered ($Δ$) and time-dependent uniform ($λ(t)$) detuning terms using exact diagonalization (ED). We show that at intermediate drive frequencies ($ω_D$), the presence of a finite $Δ$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. Such clustering is lost at special commensurate drive frequencies for which $\hbar ω_d=n Δ$ ($n \in Z$) leading to restoration of ergodicity. The violation of ETH in these driven finite-sized chains is also evident from the dynamical freezing displayed by the density-density correlation function at specific $ω_D$. Such a correlator exhibits stable oscillations with perfect revivals when driven close to the freezing frequencies for initial all spin-down ($|0\rangle$) or Neel ($|{\mathbb Z}_2\rangle$, with up-spins on even sites) states. The amplitudes of these oscillations vanish at the freezing frequencies and reduces upon increasing $Δ$; their frequencies, however, remains pinned to $Δ/\hbar$ in the large $Δ$ limit. In contrast, for the $|{\bar {\mathbb Z}_2}\rangle$ (time-reversed partner of $|{\mathbb Z}_2\rangle$) initial state, we find complete absence of such oscillations leading to freezing for a range of $ω_D$; this range increases with $Δ$. We also study the properties of quantum many-body scars in the Floquet spectrum of the model as a function of $Δ$ and show the existence of novel mid-spectrum scars at large $Δ$. We supplement our numerical results with those from an analytic Floquet Hamiltonian computed using Floquet perturbation theory (FPT) and also provide a semi-analytic computation of the quantum scar states within a forward scattering approximation (FSA).

cond-mat.str-el↗

arXiv2021

Dynamical relaxation of correlators in periodically driven integrable quantum systems

We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady state value as $n^{-(α+1)/β}$, where $n$ is the number of drive cycles and $α$ and $β$ denote positive integers. We find that generically $β=2$ within a dynamical phase characterized by a fixed $α$; however, its value can change to $β=3$ or $β=4$ either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining $β$, and chart out the values of $α$ and $β$ realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale $n_c$ which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, $ω_c$, is approached from below ($ω< ω_c$). We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.

cond-mat.stat-mech↗

arXiv2021

Minimal model for Hilbert space fragmentation with local constraints

Motivated by previous works on a Floquet version of the PXP model [Mukherjee {\it et al.} Phys. Rev. B 102, 075123 (2020), Mukherjee {\it et al.} Phys. Rev. B 101, 245107 (2020)], we study a one-dimensional spin-$1/2$ lattice model with three-spin interactions in the same constrained Hilbert space (where all configurations with two adjacent $S^z=\uparrow$ spins are excluded). We show that this model possesses an extensive fragmentation of the Hilbert space which leads to a breakdown of thermalization upon unitary evolution starting from a large class of simple initial states. Despite the non-integrable nature of the Hamiltonian, many of its high-energy eigenstates admit a quasiparticle description. A class of these, which we dub as "bubble eigenstates", have integer eigenvalues (including mid-spectrum zero modes) and strictly localized quasiparticles while another class contains mobile quasiparticles leading to a dispersion in momentum space. Other anomalous eigenstates that arise due to a {\it secondary} fragmentation mechanism, including those that lead to flat bands in momentum space due to destructive quantum interference, are also discussed. The consequences of adding a (non-commuting) staggered magnetic field and a PXP term respectively to this model, where the former preserves the Hilbert space fragmentation while the latter destroys it, are discussed. A Floquet version with time-dependent staggered field also evades thermalization with additional features like freezing of exponentially many states at special drive frequencies. Finally, we map the model to a $U(1)$ lattice gauge theory coupled to dynamical fermions and discuss the interpretation of some of these anomalous states in this language. A class of gauge-invariant states show reduced mobility of the elementary charged excitations with only certain charge-neutral objects being mobile suggesting a connection to fractons.

cond-mat.str-el↗

arXiv2021

Signatures of multifractality in a periodically driven interacting Aubry-André model

We study the many-body localization (MBL) transition of Floquet eigenstates in a driven, interacting fermionic chain with an incommensurate Aubry-André potential and a time-periodic hopping amplitude as a function of the drive frequency $ω_D$ using exact diagonalization (ED). We find that the nature of the Floquet eigenstates change from ergodic to Floquet-MBL with increasing frequency; moreover, for a significant range of intermediate $ω_D$, the Floquet eigenstates exhibit non-trivial fractal dimensions. We find a possible transition from the ergodic to this multifractal phase followed by a gradual crossover to the MBL phase as the drive frequency is increased. We also study the fermion auto-correlation function, entanglement entropy, normalized participation ratio (NPR), fermion transport and the inverse participation ratio (IPR) as a function of $ω_D$. We show that the auto-correlation, fermion transport and NPR displays qualitatively different characteristics (compared to their behavior in the ergodic and MBL regions) for the range of $ω_D$ which supports multifractal eigenstates. In contrast, the entanglement growth in this frequency range tend to have similar features as in the MBL regime; its rate of growth is controlled by $ω_D$. Our analysis thus indicates that the multifractal nature of Floquet-MBL eigenstates can be detected by studying auto-correlation function and fermionic transport of these driven chains. We support our numerical results with a semi-analytic expression of the Floquet Hamiltonian obtained using Floquet perturbation theory (FPT) and discuss possible experiments which can test our predictions.

cond-mat.dis-nn↗