arXiv subjects

Sandipan Manna

Publications and source records attributed to Sandipan Manna.

5 recordsLinked to original sources

arXiv2026

Signatures of quantum chaos and complexity in the Ising model on random graphs

We investigate signatures of quantum chaos in the mixed-field quantum Ising model on finite-size Erdős-Rényi graphs using probes scalable on near-term quantum devices. Upon tuning the graph connectivity, the system exhibits a crossover from a localized regime at low connectivity, through a chaotic regime at intermediate connectivity, to a permutation-symmetric integrable limit near all-to-all connectivity. This crossover has possible implications for the performance and trainability of variational algorithms such as QAOA. We characterize this crossover in finite-size systems using complementary probes. First, deep thermalization of a projected ensemble starting from a product state reveals slow (fast) convergence to the Haar ensemble at extremal (intermediate) connectivities. Second, we analyze eigenstate and eigenvalue correlations using the partial spectral form factor, an experimentally scalable proxy for the spectral form factor with reduced resource overhead, and observe characteristic chaos signatures at intermediate connectivities and distinct deviations at extremal connectivities. Finally, we explore the Krylov complexity of operators, a locality-independent diagnostic that, although not directly experimentally accessible, serves as a tool for quantifying scrambling. We show that it is maximized deep in the chaotic regime, corroborating the signatures observed through the experimentally scalable probes. Our results provide finite-size benchmarks demonstrating robust signatures of chaos in scalable probes and suggest that these diagnostics can be implemented in current quantum platforms to access regimes beyond classical simulation.

cond-mat.dis-nn↗

arXiv2026

Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model

We obtain the $\rm{p4m}$-symmetric Group Convolutional Neural Network (GCNN) representations of the lowest energy eigenstate of the quantum dimer model on $L{\times} L$ square-lattice in each of the ${(L^2+18L+72)}/{8}$ irreducible representations (irreps) of the lattice space group and use these to investigate the competition between columnar, plaquette and mixed phases. The networks are optimized within each irrep by minimizing the energy, which is estimated from samples obtained via an efficient directed loop sampler. In extensive benchmarks, we show excellent agreement in energy estimates, order parameters and correlation functions with exact diagonalization or quantum Monte Carlo in systems of sizes $8\leq L\leq 32$. Analysis of the scaling of the gaps in different representation sectors with systems of sizes up to $L=32$ suggest a $4$-fold degenerate ground state for $V\leq 0.4$ narrowing the regime of possible mixed/plaquette phases to $0.4 < V< 1$. Our results show that GCNN is a powerful tool to investigate ground state phase diagrams. The approach paves the way for even more accurate results by producing highly accurate variational baseline wavefunctions for quantum Monte Carlo approaches.

cond-mat.dis-nn↗

arXiv2025

Full distribution and large deviations of local observables in an exactly solvable current carrying steady state of a strongly driven XXZ chain

Current carrying steady states of interacting spin chains exhibit rich structures generated through an interplay of constraints from the Hamiltonian dynamics and those induced by the current. The \textit{XXZ} spin chain when coupled to maximally polarizing Lindblad terms (with opposite signs on either end) admits an exact solution for the steady state in a matrix product state (MPS) form. We use this exact solution to study the correlations and distributions of local spin observables in the nonequilibrium steady state. We present exact expressions for spin correlators, entropy per site and scaled cumulant generating functions (SCGF) for distributions of local observables in the \textit{XX} limit (Ising anisotropy $Δ=0$). Further, we use the exact MPS solution in the $Δ>0$ regime, to calculate numerically exact entropy, correlations, as well as full distributions of spin observables in large systems. In systems where $Δ$ is a cosine of rational multiple of $π$, we can numerically exactly estimate the large system limit of the SCGF and the large deviation/rate functions of local-$z$ magnetization. For these, we show that the deviations of the SCGF, calculated in finite systems, from the asymptotic large system size limit decay exponentially with system size; however, the decay rate is a discontinuous function of $Δ$. The $x$ magnetization density shows a double peak structure at $Δ\lesssim 1$, suggesting short-range ferromagnetic ordering in the $x$ direction similar to what was reported for the ground state of the XXZ chain.

cond-mat.stat-mech↗

arXiv2025

Projected ensemble in a system with conserved charges with local support

The investigation of ergodicity or lack thereof in isolated quantum many-body systems has conventionally focused on the description of the reduced density matrices of local subsystems in the contexts of thermalization, integrability, and localization. Recent experimental capabilities to measure the full distribution of quantum states in Hilbert space and the emergence of specific state ensembles have extended this to questions of {\textit{deep thermalization}}, by introducing the notion of the {\textit{projected ensemble}} -- ensembles of pure states of a subsystem obtained by projective measurements on its complement. While previous work examined chaotic unitary circuits, Hamiltonian evolution, and systems with global conserved charges, we study the projected ensemble in systems where there are an extensive number of conserved charges all of which have (quasi)local support. We employ a strongly disordered quantum spin chain which shows many-body localized dynamics over long timescales as well as the $\ell$-bit model, a phenomenological archetype of a many-body localized system, with the charges being $1$-local in the latter. In particular, we discuss the dependence of the projected ensemble on the measurement basis. Starting with random direct product states, we find that the projected ensemble constructed from time-evolved states converges to a Scrooge ensemble at late times and in the large system limit except when the measurement operator is close to the conserved charges. This is in contrast to systems with global conserved charges where the ensemble varies continuously with the measurement basis. We relate these observations to the emergence of Porter-Thomas distribution in the probability distribution of bitstring measurement probabilities.

cond-mat.stat-mech↗

arXiv2023

Thermal Drude weight in an integrable chiral clock model

We calculate the finite temperature thermal conductivity of a time-reversal invariant chiral $\mathbb{Z}_3$ clock model along an integrable line in the parameter space using tDMRG. The thermal current itself is not a conserved charge, unlike in the XXZ model, but has a finite overlap with a local conserved charge $Q^{(2)}$ obtained from the transfer matrix. We find that the Drude weight is finite at non-zero temperature, and the Mazur bound from $Q^{(2)}$ saturates the Drude weight, allowing us to obtain an asymptotic expression for the Drude weight at high temperatures. The numerical estimates are validated using a sum rule for thermal conductivity. On the computational side, we also explore the effectiveness of the ancilla disentangler in the integrable and non-integrable regimes of the model. We find that the disentangler helps in localizing the entanglement growth around the quench location, but the improvement is lesser in the non-integrable regime and at low temperatures.

cond-mat.stat-mech↗