Quantum dynamics in transverse-field Ising models from classical networks

Abstract

The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.

Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain

“…Since the DQPT is associated with an unstable fixed point and thus with a divergent correlation length, it is natural to expect that the dynamics of spin-spin correlations is strongly influenced by the underlying DQPT. We find that spin-spin correlations show a marked signature of the DQPTs in that they become maximal whenever a DQPT occurs, as observed also in other contexts 8,16 .…”

“…We know that we can formally consider the Loschmidt amplitude as a complex partition function, see Eq. (16), meaning that the formalism introduced in Section VI A can be used also in the nonequilibrium context, taking into account that the Hamiltonian H is now complex, see Eq. (14).…”

“…G(µ, t) can be exactly solved using the method introduced in Section V , see Eqs. (16), (20), (21), leading in the thermodynamic limit N → ∞ to the expression:…”

Efficiently solving the dynamics of many-body localized systems at strong disorder

“…Overall, our method maps the dynamical quantum many-body problem onto a system of classical degrees of freedom of mutually commuting operators, similar in spirit to recent works where dynamical problems have been solved using classical [85] or artificial neural networks [86]. Instead of solving the problem in the basis of the bare particles, our work shows that a simple basis transformation onto more convenient degrees of freedom can improve the accuracy and efficiency dramatically, which might also be of relevance for the aforementioned approaches.…”

Learning phase transitions from dynamics

“…This approach has enabled the autonomous detection of order parameters [2,5,6], phase transitions [1,3], and entire phase diagrams [4,7,16,17]. Simultaneous research effort at the interface between machine learning and many-body physics has focused on the use of neural networks for efficient representations of quantum wave functions [18][19][20][21][22][23][24][25][26], drawing a parallel between deep networks and the renormalization group [27][28][29]. Overall, these studies exemplify the power of machine learning for extracting information from physical data without detailed physical input.…”