arXiv subjects

Zoltán Zimborás

Publications and source records attributed to Zoltán Zimborás.

83 records · Page 5Linked to original sources

arXiv2017

The bilinear-biquadratic model on the complete graph

We study the spin-1 bilinear-biquadratic model on the complete graph of N sites, i.e., when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be rewritten as the linear combination of the quadratic Casimir operators of su(3) and su(2). Using group representation theory, we explicitly diagonalize the Hamiltonian and map out the ground-state phase diagram of the model. Furthermore, the complete energy spectrum, with degeneracies, is obtained analytically for any number of sites.

cond-mat.stat-mech↗

arXiv2017

Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information

We study the dynamics of the transverse field Ising chain after a local quench in which two independently thermalised chains are joined together and are left to evolve unitarily. In the emerging non-equilibrium steady state the Rényi mutual information with different indices are calculated between two adjacent segments of the chain, and are found to scale logarithmically in the subsystem size. Surprisingly, for Rényi indices $α>2$ we find cases where the prefactor of the logarithmic dependence is negative. The fact that the naively defined Rényi mutual information might be negative has been pointed out before, however, we provide the first example for this scenario in a realistic many-body setup. Our numerical and analytical results indicate that in this setup it can be negative for any index $α>2$ while it is always positive for $α<2.$ Interestingly, even for $α>2$ the calculated prefactors show some universal features: for example, the same prefactor is also shown to govern the logarithmic time dependence of the Rényi mutual information before the system relaxes locally to the steady state. In particular, it can decrease in the non-equilibrium evolution after the quench.

cond-mat.stat-mech↗

arXiv2017

Universal extensions of restricted classes of quantum operations

For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises the question of what additional unitary gates should be added to a given gate-set in order to attain physical universality, i.e., to be able to perform arbitrary unitary transformation on the relevant Hilbert space. In this work, we study this problem for three paradigmatic cases of naturally occurring restricted gate-sets: (A) particle-number preserving bosonic linear optics, (B) particle-number preserving fermionic linear optics, and (C) general (not necessarily particle-number preserving) fermionic linear optics. Using tools from group theory and control theory, we classify, in each of these scenarios, what sets of gates are generated, if an additional gate is added to the set of allowed transformations. This allows us to solve the universality problem completely for arbitrary number of particles and for arbitrary dimensions of the single-particle Hilbert space.

quant-ph↗

arXiv2016

Entanglement negativity in two-dimensional free lattice models

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case, we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.

cond-mat.stat-mech↗

arXiv2016

Chiral Quantum Walks

Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time-symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time-asymmetry. Moreover, we show that time-asymmetry in circuits can be controlled using local gates only, and can simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport, and imply that time-asymmetry represents an omnipresent yet poorly understood effect in quantum information science.

quant-ph↗

arXiv2015

Symmetry criteria for quantum simulability of effective interactions

What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of simulation and permit a reasoning beyond the limitations of the usual explicit Lie closure. Conserved quantities induced by symmetries pave the way to a resource theory for simulability. On a general level, one can now decide equality for any pair of compact Lie algebras just given by their generators without determining the algebras explicitly. Several physical examples are illustrated, including entanglement invariants, the relation to unitary gate membership problems, as well as the central-spin model.

quant-ph↗

arXiv2015

On squares of representations of compact Lie algebras

We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.

math-ph↗

arXiv2014

On the NP-completeness of the Hartree-Fock method for translationally invariant systems

The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem, is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, as characterized by its worst-case behavior, the HF problem is NP-complete. In this work, we map out boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases the self-consistent field method is computationally feasible and when it is not.

quant-ph↗

arXiv2013

A Dynamic Systems Approach to Fermions and Their Relation to Spins

Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully controllable and quasifree cases, as well as various translation-invariant and particle-number conserving cases. We determine the respective dynamic system Lie algebras to express reachable sets of pure (and mixed) states by explicit orbit manifolds.

quant-ph↗

arXiv2010

Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata

We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, like quasifree and stabilizer states. Finally we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.

quant-ph↗

arXiv2007

Entanglement entropy in aperiodic singlet phases

We study the average entanglement entropy of blocks of contiguous spins in aperiodic XXZ chains which possess an aperiodic singlet phase at least in a certain limit of the coupling ratios. In this phase, where the ground state constructed by a real space renormalization group method, consists (asymptotically) of independent singlet pairs, the average entanglement entropy is found to be a piecewise linear function of the block size. The enveloping curve of this function is growing logarithmically with the block size, with an effective central charge in front of the logarithm which is characteristic for the underlying aperiodic sequence. The aperiodic sequence producing the largest effective central charge is identified, and the latter is found to exceed the central charge of the corresponding homogeneous model. For marginal aperiodic modulations, numerical investigations performed for the XX model show a logarithmic dependence, as well, with an effective central charge varying continuously with the coupling ratio.

cond-mat.stat-mech↗