Light cone tensor network and time evolution

Abstract

The transverse folding algorithm [Phys. Rev. Lett. 102, 240603] is a tensor network method to compute time-dependent local observables in out-of-equilibrium quantum spin chains that can sometimes overcome the limitations of matrix product states. We present a contraction strategy that makes use of the exact light cone structure of the tensor network representing the observables. The strategy can be combined with the hybrid truncation proposed for global quenches in [Phys. Rev. A 91, 032306], which significantly improves the efficiency of the method. We demonstrate the performance of this transverse light cone contraction also for transport coefficients, and discuss how it can be extended to other dynamical quantities.

Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality

“…Specifically, we study the dynamics of the negativity between the regions A and B under a tripartition ABC in generic one-dimensional systems with discrete spacetime and local interactions, i.e., local quantum circuits. Combining a replica trick [46,50] with a space-time duality approach [14][15][16][73][74][75][76][77][78][79][80][81][82][83][84][85], we provide a simple expression for the negativity, which is applicable for times smaller than the sizes of the regions A, B, C. We then use this expression to show that, up to exponentially small corrections, the negativity coincides with the Rényi-1/2 mutual information divided by two. This result holds for any local quantum circuit with translation symmetry in space, irrespective of the nature of the dynamics.…”

Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain

“…Furthermore, our algorithm is complementary to those proposed for spin-boson models: it avoids both explicit memory-range cutoffs and long-range interacting gates. We note that further improvements are likely possible: one possibility is to exploit the approach of Schuch and Bauer [117], which uses Gaussian MPS representations of Gaussian states; in a different direction, chain mappings through orthogonal polynomials [118] developed in the context of open quantum systems could be combined with efficient versions of the IM approach for one-dimensional systems [74,75].…”

“…as a MPS by numerically contracting corresponding tensor networks. This approach can be made efficient [74,75] provided temporal entanglement of the IM remains low. In certain 1d Floquet spin models, the low TE of the IM was established, via either exact solutions or numerical simulations [71,[76][77][78][79][80][81].…”

Wilson loops in the Hamiltonian formalism

“…Smilga and others argued that thermal solitons are unphysical [71][72][73][74], I suggest that they represent new, collective excitations at T = 0, which evaporate smoothly as T → 0. This can be studied numerically at nonzero temperature in real time, using either tensor networks on a classical computer [104][105][106][107], or even with the noisy intermediate-scale quantum computers which are available at present. This is similar to studying the screening of background electric fields at nonzero θ [108][109][110][111][112][113][114][115][116][117].…”

“…In particular, deep inelastic scattering is usually described by the propagation of time-like Wilson lines [18]. My approach can be adapted to the light-front directly [106,107,118], especially using quantum computers [119][120][121].…”