arXiv subjects

Luca Tagliacozzo

Publications and source records attributed to Luca Tagliacozzo.

At least 19 recordsLinked to original sources

arXiv2026

Pulling strings in real time: flux tube dynamics in (2+1)-d $\mathbb{Z}_2$-Higgs Gauge Theories

Understanding real-time flux-tube dynamics in more than one spatial dimension is key to unlocking the non-perturbative physics of confinement, and is now actively pursued by quantum computing and simulation experiments. However, describing such dynamics has proven to be extremely challenging with both experiments and state-of-the-art numerical simulations limited to small volumes and short timescales. Here we investigate flux tube statics and real-time evolution in a genuine two-dimensional $\mathbb{Z}_2$ Higgs gauge theory at system sizes and timescales order of magnitude beyond present experiments and numerics. The key enabling element is the recently introduced Clifford-augmented matrix product states (CAMPS) framework, which we demonstrate to parametrically reduce the entanglement that must be represented in the matrix product state; both in the pure-gauge limit and in the presence of dynamical matter. We benchmark this capability through stringent tests of effective string theory, including universal spectral features and flux tube roughening properties in presence of matter. We then introduce a string-pull protocol that selectively excites transverse modes and reconstructs their finite-size spectrum in real time. In the rough regime, the response is collective, and our simulations show that this is also well captured by universal effective string theory predictions. Strong confinement instead produces long-lived, lattice-locked local dynamics persisting to times $tJ \gtrsim 100$. These results provide ab initio evidence that effective string theory captures nonequilibrium string dynamics and reveal a hitherto unexplored long-lived prethermal regime of strongly confined flux tubes, providing a novel angle on how confinement dictates dynamics in more than one spatial dimension.

quant-ph↗

arXiv2026

Universal scaling framework for parameterized quantum evolutions at criticality

Variational ans\"atze are a cornerstone of quantum many-body physics, providing compact approximations to complex ground states using finite resources. Recent quantum-technology advances have introduced a new class based on layered parameterized evolutions. Assessing whether they can represent critical ground states is challenging: correlations span all length scales, while finite circuit depth limits how far they extend. Building on finite-resource scaling from tensor networks, we assign each ansatz an emergent correlation length $\xi_D$, the longest range over which it faithfully captures critical correlations. Its growth with refinement parameter $D$, $\xi_D \propto D^\kappa$, defines an exponent $\kappa$ measuring how efficiently an architecture converts resources into long-distance correlations. Applying this framework to the critical transverse-field Ising model, with $D$ the circuit depth of parameterized evolutions, we compare ans\"atze with nearest-neighbor and long-range generators, and layers where generators act separately or combined. All ans\"atze are compatible with algebraic growth, but fitted exponents range from $\kappa\simeq1$ to $\kappa\simeq3$. Exponential interactions give the largest exponents, while power-law interactions stay close to nearest-neighbor behavior, showing long-range support alone gives no scaling advantage. Combined-generator layers generally outperform separable ones, so layer organization matters alongside interaction range. Finally, a quasiparticle analysis shows finite depth leaves an unresolved window of width $\xi_D^{-1}$ around the low-energy modes responsible for long-distance correlations. The emergent correlation length thus acts as an infrared resolution scale, providing a benchmark for critical-state preparation and a guide for designing resource-efficient variational architectures.

quant-ph↗

arXiv2026

Extracting conformal data from Loschmidt echoes after critical quenches

Conformal field theory provides universal predictions for Loschmidt amplitudes following quenches from product states to critical Hamiltonians. Building on this observation, we develop a route to extracting conformal data from real-time dynamics without preparing critical low-energy states. After analytic continuation, the Loschmidt amplitude is described by a boundary-CFT partition function on a strip, whose transverse transfer matrix encodes both the boundary operator spectrum and the central charge. Local space-time perturbations of the amplitude are governed by equilibrium correlation functions, and therefore provide access to critical exponents. In parallel, generalized temporal entropies exhibit scaling with time analogous to the equilibrium scaling of spatial entanglement entropy. We show that the low-lying boundary spectrum can be reconstructed from the system-size dependence of finite-chain Loschmidt echoes, whose damped oscillations encode differences of boundary scaling dimensions. Finally, we propose a finite-size scaling protocol that can extract these quantities from simulations or experiments on state-of-the-art quantum platforms.

quant-ph↗

arXiv2026

Mapping twist fields to local operators via tensor networks

Twist fields are a powerful formal tool to compute R\'enyi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly accessible in experiments. In this work, we construct explicit local operators acting on the physical Hilbert space whose expectation values reproduce the action of twist fields in matrix product states. Our construction is exact in the injectivity limit and when the tensor is chosen at the center of orthogonality, and provides a direct operational method to evaluate R\'enyi entropies without accessing auxiliary tensor indices. We test our formulation numerically in the transverse-field Ising model, demonstrating rapid convergence to the exact entanglement entropy as the injectivity scale is reached. Furthermore, we show that twist operators determined from relatively small reference systems can be reliably transferred to larger systems, once the reference size exceeds a characteristic scale set by the correlation length. Since the resulting operators admit a decomposition in terms of a finite number of local observables, our results provide a scalable and experimentally accessible framework to probe entanglement in quantum simulators.

quant-ph↗

arXiv2026

Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems

We study temporal correlations in interacting quantum systems through the influence functional of a half-infinite quantum Ising chain. Using R\'enyi entropies and temporal mutual information, we confirm that integrable dynamics is captured by the quasiparticle picture. In contrast, generic ergodic Hamiltonian dynamics exhibits pronounced deviations from random-circuit universality, and its generalization including a symmetry accounting for energy conservation. Instead, we find a long mesoscopic regime suggestive of a slow spectral reorganization of the influence functional. Our results reveal a rich temporal structure in generic Hamiltonian dynamics and point to limitations of existing random-circuit paradigms at experimentally and numerically relevant timescales.

quant-ph↗

arXiv2026

Interface roughening in the 3-D Ising model with tensor networks

Interfaces in three-dimensional many-body systems can exhibit rich phenomena beyond the corresponding bulk properties. In particular, they can fluctuate and give rise to massless low energy degrees of freedom even in the presence of a gapped bulk. In this work, we present the first tensor-network study of the paradigmatic interface roughening transition of the 3-D Ising model using highly asymmetric lattices that are infinite in the $(xy)$ direction and finite in $z$. By reducing the problem to an effective 2-D tensor network, we study how truncating the $z$ direction reshapes the physics of the interface. For a truncation based on open boundary conditions, we demonstrate that varying the interface width gives rise to either a $\mathbb{Z}_2$ symmetry breaking transition (for odd $L_z$) or a smooth crossover(for even $L_z$). For antiperiodic boundary conditions, we obtain an effective $\mathbb{Z}_q$ clock model description with $q=2L_z$ that exhibits an intermediate Luttinger liquid phase with an emergent $\U(1)$ symmetry.

cond-mat.str-el↗

arXiv2025

Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder

We revisit the U(1) quantum link model in a ladder geometry, finding, by finite-size scaling, that the critical exponent $\nu=1$ and the central charge $c=1/2$ are consistent with the Ising universality class for all phase transitions observed. A blind application of the Harris criterion would suggest that this criticality is lost in the presence of the disorder. It turns out not to be the case. For the disorder affecting ladder's rung hoppings only, we have found that the transitions survive disappearing only for quite strong disorder. The disorder in the ladder's legs destroys the nonzero mass phase criticality, while the symmetry-protected topological phase for zero mass survives a small disorder. The observed robustness against disorder is explained qualitatively using field-theoretic arguments.

cond-mat.dis-nn↗

arXiv2025

Quantics Tensor Train for solving Gross-Pitaevskii equation

We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutta integrator for real-time dynamics. The framework captures a broad range of physical scenarios - including barrier-confined condensates, quasi-random potentials, long-range dipolar interactions, and multicomponent spinor dynamics - without leaving the compressed representation. Relative to standard discretizations, the QTT approach achieves an exponential reduction in computational resources while retaining quantitative accuracy, thereby extending the practicable regime of Gross-Pitaevskii simulations on classical hardware. These results position tensor networks as a practical bridge between high-performance classical computing and prospective quantum hardware for the numerical treatment of nonlinear Schrodinger-type partial differential equations.

cond-mat.quant-gas↗

arXiv2025

Overcoming the entanglement barrier with sampled tensor networks

The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier} restricts classical simulations and, conversely, underpins the quantum advantage anticipated from future devices. Here we show that, for one-dimensional Hamiltonian dynamics, the spatio-temporal tensor network encoding the evolved wave function amplitudes can be contracted efficiently along the left-right (spatial) direction. Exploiting this structure, we develop a hybrid Tensor-Network/Monte-Carlo (TN-MC) algorithm that samples the wave function and evaluates expectation values of generic local operators with computational cost that scales only polynomially in time. The accurate contraction of the wave function amplitudes is a consequence of the favorable scaling with time of the generalised temporal entropies. We find that their real part either saturates or, at most, grows logarithmically with time, revealing new instances of continuous dynamical quantum phase transitions (DQPTs) which we characterize. Our results therefore show that, when computing expectation values of local operators, the entanglement barrier in one-dimensional Hamiltonian evolution can be bypassed with a TN-MC blend.

quant-ph↗

arXiv2025

Spatio-temporal tensor-network approaches to out-of-equilibrium dynamics bridging open and closed systems

The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better contraction strategies for the full spatio-temporal tensor networks that encode the path integral of the dynamics, as well as the conceptual integration of influence functionals, process tensors, and transfer matrices within the tensor network formalism. We discuss recent algorithmic developments, highlight the complexity of influence functionals in various dynamical regimes and present consistent results of different communities, showing how ergodic dynamics render these functionals exponentially difficult to compress. Finally, we provide an outlook on strategies to encode complementary influence functional overlaps, paving the way for accurate descriptions of open and closed quantum systems with tensor networks.

quant-ph↗

arXiv2024

A tensor network formulation of Lattice Gauge Theories based only on symmetric tensors

The Lattice Gauge Theory Hilbert space is divided into gauge-invariant sectors selected by the background charges. Such a projector can be directly embedded in a tensor network ansatz for gauge-invariant states as originally discussed in [Phys. Rev. B 83, 115127 (2011)] and in [Phys. Rev. X 4, 041024 (2014)] in the context of PEPS. The original ansatz is based on sparse tensors, though parts of them are not explicitly symmetric, and thus their actual implementation in numerical simulations has been hindered by the complexity of developing ad hoc libraries. Here we provide a new PEPS tensor network formulation of gauge-invariant theories purely based on symmetric elementary tensors. The new formulation can be implemented in numerical simulation using available state-of-the-art tensor network libraries but also holds interest from a purely theoretical perspective since it requires embedding the original gauge theory with gauge symmetry G into an enlarged globally symmetric theory with symmetry GxG. By revisiting the original ansatz in the modern landscape of i) duality transformations between gauge and spin systems, ii) finite depth quantum circuits followed by measurements that allow generating topologically ordered states, and iii) Clifford enhanced tensor networks, we show that such a new formulation provides a novel duality transformation between lattice gauge theories and specific sectors of globally invariant systems.

hep-lat↗

arXiv2024

Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling

We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension $\chi$ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the $\chi$-independent universal transfer matrix's gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory. This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing $\chi$, the infrared scale, set by the correlation length $\xi(\chi)$, increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidences from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.

cond-mat.stat-mech↗

arXiv2024

Pauli weight requirement of the matrix elements in time-evolved local operators: dependence beyond the equilibration temperature

The complexity of simulating the out-of-equilibrium evolution of local operators in the Heisenberg picture is governed by the operator entanglement, which grows linearly in time for generic non-integrable systems, leading to an exponential increase in computational resources. A promising approach to simplify this challenge involves discarding parts of the operator and focusing on a subspace formed by "light" Pauli strings - strings with few Pauli matrices - as proposed by Rakovszki et al. [PRB 105, 075131 (2022)]. In this work, we investigate whether this strategy can be applied to quenches starting from homogeneous product states. For ergodic dynamics, these initial states grant access to a wide range of equilibration temperatures. By concentrating on the desired matrix elements and retaining only the portion of the operator that contains Pauli strings parallel to the initial state, we uncover a complex scenario. In some cases, the light Pauli strings suffice to describe the dynamics, enabling efficient simulation with current algorithms. However, in other cases, heavier strings become necessary, pushing computational demands beyond our current capabilities. We analyze this behavior using a newly introduced measure of complexity, the Operator Weight Entropy, which we compute for different operators across most points on the Bloch sphere.

quant-ph↗

arXiv2024

Measuring temporal entropies in experiments

We propose a novel experimental protocol to measure generalized temporal entropies in many-body quantum systems. Our approach involves using local operators as probes to characterize the out-of-equilibrium dynamics induced by a geometric double quench on a replicated system. Such protocol mimics the path-integral on the corresponding Riemann surface encoding generalized temporal entanglement. We present the results of tensor network simulations of one-dimensional systems which validate the protocol and demonstrate the experimental feasibility of measuring generalized temporal entropies, and we outline the experimental requirements for implementing these quenches using state-of-the-art quantum simulators. Therefore, our results provide a physical interpretation of the meaning of generalized temporal entropies. Furthermore, they reveal that the dynamics induced on two replicas of the Ising model in a transverse field differ qualitatively from the ones of its non-integrable extension, suggesting that generalized temporal entropies can be used as a tool for identifying different dynamical classes in quantum systems.

quant-ph↗

arXiv2024

Pseudospectral method for solving PDEs using Matrix Product States

This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating Functionals (HDAF) to MPS, a highly accurate pseudospectral method for approximating functions of derivatives. Integrating HDAF into an MPS finite precision algebra, we test four types of quantum-inspired algorithms for time evolution: explicit Runge-Kutta methods, Crank-Nicolson method, explicitly restarted Arnoli iteration and split-step. The benchmark problem is the expansion of a particle in a quantum quench, characterized by a rapid increase in space requirements, where HDAF surpasses traditional finite difference methods in accuracy with a comparable cost. Moreover, the efficient HDAF approximation to the free propagator avoids the need for Fourier transforms in split-step methods, significantly enhancing their performance with an improved balance in cost and accuracy. Both approaches exhibit similar error scaling and run times compared to FFT vector methods; however, MPS offer an exponential advantage in memory, overcoming vector limitations to enable larger discretizations and expansions. Finally, the MPS HDAF split-step method successfully reproduces the physical behavior of a particle expansion in a double-well potential, demonstrating viability for actual research scenarios.

quant-ph↗

arXiv2024

Gapless deconfined phase in a $\mathbb{Z}_N$ symmetric Hamiltonian created in a cold-atom setup

We investigate a quasi-two-dimensional system consisting of two species of alkali atoms confined in a specific optical lattice potential [Phys. Rev. A 95, 053608 (2017)]. In the low-energy regime, this system is governed by a unique $\mathbb{Z}_N$ gauge theory, where field theory arguments have suggested that it may exhibit two exotic gapless deconfined phases, namely a dipolar liquid phase and a Bose liquid phase, along with two gapped (confined and deconfined) phases. We address these predictions numerically by using large-scale density matrix renormalization group simulations. Our findings provide conclusive evidence for the existence of a gapless Bose liquid phase for $N \geq 7$. We demonstrate that this gapless phase shares the same critical properties as one-dimensional critical phases, resembling weakly coupled chains of Luttinger liquids. In the range of ladder and cylinder geometries and $N$ considered, the gapless dipolar phase predicted theoretically is still elusive and its characterization will probably require a full two-dimensional treatment.

cond-mat.str-el↗

arXiv2024

Chebyshev approximation and composition of functions in matrix product states for quantum-inspired numerical analysis

This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw evaluations to represent analytic and highly differentiable functions as MPS Chebyshev interpolants. It demonstrates rapid convergence for highly-differentiable functions, aligning with theoretical predictions, and generalizes efficiently to multidimensional scenarios. The performance of the algorithm is compared with that of tensor cross-interpolation (TCI) and multiscale interpolative constructions through a comprehensive comparative study. When function evaluation is inexpensive or when the function is not analytical, TCI is generally more efficient for function loading. However, the proposed method shows competitive performance, outperforming TCI in certain multivariate scenarios. Moreover, it shows advantageous scaling rates and generalizes to a wider range of tasks by providing a framework for function composition in MPS, which is useful for non-linear problems and many-body statistical physics.

quant-ph↗

arXiv2024

Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point

We show how the Loschmidt echo of a product state after a quench to a conformal invariant critical point and its leading finite time corrections can be predicted by using conformal field theories (CFT). We check such predictions with tensor networks, finding excellent agreement. As a result, we can use the Loschmidt echo to extract the universal information of the underlying CFT including the central charge, the operator content, and its generalized temporal entropies. We are also able to predict and confirm an emerging dual-unitarity of the evolution at late times, since the spatial transfer matrix operator that evolves the system in space becomes unitary in such limit. Our results on the growth of temporal entropies also imply that, using state-of-the art tensor networks algorithms, such calculations only require resources that increase polynomially with the duration of the quench, thus providing an example of numerically efficiently solvable out-of-equilibrium scenario.

cond-mat.stat-mech↗