arXiv subjects

Miha Srdinšek

Publications and source records attributed to Miha Srdinšek.

4 recordsLinked to original sources

arXiv2026

Hybrid between biologically and quantum-inspired many-body states

Deep neural networks can represent very different sorts of functions, including complex quantum many-body states. Tensor networks can also represent these states, have more structure and are easier to optimize. However, they can be prohibitively costly computationally in two or higher dimensions. Here, we propose a generalization of the perceptron -- the perceptrain -- which borrows features from the two different formalisms. We construct variational many-body ansatz from a simple network of perceptrains. The network can be thought of as a neural network with a few distinct features inherited from tensor networks. These include efficient local optimization akin to the density matrix renormalization algorithm, instead of optimizing all the parameters at once; the possibility to dynamically increase the number of parameters during the optimization; the possibility to compress the state; and a structure that remains quantum-inspired. We showcase the ansatz using a combination of variational Monte Carlo (VMC) and Green function Monte Carlo (GFMC) on a $10\times 10$ transverse field quantum Ising model with a long-range $1/r^6$ antiferromagnetic interaction. The model corresponds to the Rydberg (cold) atoms platform proposed for quantum annealing. We consistently find a very high relative accuracy for the ground state energy, around $10^{-5}$ for VMC and $10^{-6}$ for GFMC in all regimes of parameters, including in the vicinity of the quantum phase transition. We use very small ranks ($\sim 2$-$5$) of perceptrains, as opposed to multiples of thousand used in matrix product states. The optimization of the energy was very robust. The entire phase diagram was found with a single initial condition and a fixed set of hyperparameters.

cond-mat.str-el↗

arXiv2024

Ergodicity breaking and deviation from Eigenstate Thermalisation in relativistic QFT

The validity of the ergodic hypothesis in quantum systems can be rephrased in the form of the eigenstate thermalisation hypothesis (ETH), a set of statistical properties for the matrix elements of local observables in energy eigenstates, which is expected to hold in any ergodic system. We test the ETH in a nonintegrable model of relativistic quantum field theory (QFT) using the numerical method of Hamiltonian truncation in combination with analytical arguments based on Lorentz symmetry and renormalisation group theory. We find that there is an infinite sequence of eigenstates with the characteristics of quantum many-body scars, that is, exceptional eigenstates with observable expectation values that lie far from thermal values, and we show that these states are one-quasiparticle states. We argue that in the thermodynamic limit the eigenstates cover the entire area between two diverging lines: the line of one-quasiparticle states, whose direction is dictated by relativistic kinematics, and the thermal average line. Our results suggest that the strong version of the ETH is violated in any relativistic QFT whose spectrum admits a quasiparticle description.

cond-mat.stat-mech↗

arXiv2023

Rényi entropy of quantum anharmonic chain at non-zero temperature

The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the Rényi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the Rényi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the $ϕ^4$ model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes - para, disordered and quasi long-range ordered -, met as the interaction is increased. The Rényi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the Rényi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all $ϕ^4$-like systems, as well as in the elusive water ice transition across phases VII, VIII and X.

cond-mat.stat-mech↗

arXiv2022

Quantum Rényi entropy by optimal thermodynamic integration paths

Despite being a well-established operational approach to quantify entanglement, Rényi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic integration scheme, where the Rényi entropy can be efficiently evaluated using regularizing paths. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate it in the one-dimensional quantum Ising model and perform the evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature.

cond-mat.stat-mech↗