arXiv subjects

Paolo Zanardi

Publications and source records attributed to Paolo Zanardi.

At least 91 records · Page 5Linked to original sources

arXiv2009

Fidelity in topological quantum phases of matter

Quantum phase transitions that take place between two distinct topological phases remain an unexplored area for the applicability of the fidelity approach. Here, we apply this method to spin systems in two and three dimensions and show that the fidelity susceptibility can be used to determine the boundary between different topological phases particular to these models, while at the same time offering information about the critical exponent of the correlation length. The success of this approach relies on its independence on local order parameters or breaking symmetry mechanisms, with which non-topological phases are usually characterized. We also consider a topological insulator/superconducting phase transition in three dimensions and point out the relevant features of fidelity susceptibility at the boundary between these phases.

cond-mat.str-el↗

arXiv2009

Fidelity approach to the disordered quantum XY model

We study the random XY spin chain in a transverse field by analyzing the susceptibility of the ground state fidelity, numerically evaluated through a standard mapping of the model onto quasi-free fermions. It is found that the fidelity susceptibility and its scaling properties provide useful information about the phase diagram. In particular it is possible to determine the Ising critical line and the Griffiths phase regions, in agreement with previous analytical and numerical results.

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arXiv2008

Thermal states of the Kitaev honeycomb model: a Bures metric analysis

We analyze the Bures metric over the canonical thermal states for the Kitaev honeycomb mode. In this way the effects of finite temperature on topological phase transitions can be studied. Different regions in the parameter space of the model can be clearly identified in terms of different temperature scaling behavior of the Bures metric tensor. Furthermore, we show a simple relation between the metric elements and the crossover temperature between the quasi-critical and the quasi-classical regions. These results extend the ones of [29,30] to finite temperatures.

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arXiv2008

Quantum criticality as a resource for quantum estimation

We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and λis the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order 1/L may be achieved in the estimation of λat the critical point compared to the non-critical case. We show that analogue results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).

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arXiv2008

Operator fidelity susceptibility, decoherence and quantum criticality

The extension of the notion of quantum fidelity from the state-space level to the operator one can be used to study environment-induced decoherence. state-dependent operator fidelity sucepti- bility (OFS), the leading order term for slightly different operator parameters, is shown to have a nontrivial behavior when the environment is at critical points. Two different contributions to OFS are identified which have distinct physical origins and temporal dependence. Exact results for the finite-temperature decoherence caused by a bath described by the Ising model in transverse field are obtained.

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arXiv2008

Universal sub-leading terms in ground state fidelity

The study of the (logarithm of the) {\em fidelity} i.e., of the overlap amplitude, between ground states of Hamiltonians corresponding to different coupling constants, provides a valuable insight on critical phenomena. When the parameters are infinitesimally close, it is known that the leading term behaves as $O(L^α)$ ($L$ system size) where $α$ is equal to the spatial dimension $d$ for gapped systems, and otherwise depends on the critical exponents. Here we show that when parameters are changed along a critical manifold, a sub-leading O(1) term can appear. This term, somewhat similar to the topological entanglement entropy, depends only on the system's universality class and encodes non-trivial information about the topology of the system. We relate it to universal $g$ factors and partition functions of (boundary) conformal field theory in $d=1$ and $d=2$ dimensions. Numerical checks are presented on the simple example of the XXZ chain.

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arXiv2008

Bang-Bang control of a qubit coupled to a quantum critical spin bath

We analytically and numerically study the effects of pulsed control on the decoherence of a qubit coupled to a quantum spin bath. When the environment is critical, decoherence is faster and we show that the control is relatively more effective. Two coupling models are investigated, namely a qubit coupled to a bath via a single link and a spin star model, yielding results that are similar and consistent.

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arXiv2008

Fidelity analysis of topological quantum phase transitions

We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical models; we exploit this mapping to obtain the scaling of the fidelity metric tensor near criticality. The topological phase transitions manifest themselves in divergences of the fidelity metric across the phase boundaries. These results provide evidence that the fidelity approach is a valuable tool to investigate novel phases lacking a clear characterization in terms of local order parameters.

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arXiv2007

Quantum Chernoff Bound metric for the XY model at finite temperature

We explore the finite temperature phase diagram of the anisotropic XY spin chain using the Quantum Chernoff Bound metric on thermal states. The analysis of the metric elements allows to easily identify, in terms of different scaling with temperature, quasi-classical and quantum-critical regions. These results extend recent ones obtained using the Bures metric and show that different information-theoretic notions of distance can carry the same sophisticated information about the phase diagram of an interacting many-body system featuring quantum-critical points.

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arXiv2007

Bures metric over thermal state manifolds and quantum criticality

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows to complement the understanding of the phase diagram including cross-over regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.

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arXiv2007

Quantum critical scaling of the geometric tensors

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.

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arXiv2007

String and Membrane condensation on 3D lattices

In this paper, we investigate the general properties of lattice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three 3D spin models which lead to Z_2 gauge theory at low energies. All the three models are exactly soluble and produce topologically ordered ground states. The first model contains both closed-string and closed-membrane condensations. The second model contains closed-string condensation only. The ends of open-strings behave like fermionic particles. The third model also has condensations of closed membranes and closed strings. The ends of open strings are bosonic while the edges of open membranes are fermionic. The third model contains a new type of topological order.

cond-mat.str-el↗

arXiv2006

Mixed-state fidelity and quantum criticality at finite temperature

We extend to finite temperature the fidelity approach to quantum phase transitions (QPTs). This is done by resorting to the notion of mixed-state fidelity that allows one to compare two density matrices corresponding to two different thermal states. By exploiting the same concept we also propose a finite-temperature generalization of the Loschmidt echo. Explicit analytical expressions of these quantities are given for a class of quasi-free fermionic Hamiltonians. A numerical analysis is performed as well showing that the associated QPTs show their signatures in a finite range of temperatures.

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arXiv2006

Ground state overlap and quantum phase transitions

We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.

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arXiv2006

Fidelity optimization for holonomic quantum gates in dissipative environments

We analyze the performance of holonomic quantum gates in semi-conductor quantum dots, driven by ultrafast lasers, under the effect of a dissipative environment. In agreement with the standard practice, the environment is modeled as a thermal bath of oscillators linearly coupled with the excitonic states of the quantum dot. Standard techniques of quantum dissipation make the problem amenable to a numerical treatment and allow to determine the fidelity (the common gate-performance estimator), as a function of all the relevant physical parameters. As a consequence of our analysis, we show that, by varying in a suitable way the controllable parameters, the disturbance of the environment can be (approximately) suppressed, and the performance of the gate optimized--provided that the thermal bath is purely superhomic. We conclude by showing that such an optimization it is impossible for ohmic environments.

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arXiv2005

Coupling bosonic modes with a qubit: entanglement dynamics at zero and finite-temperatures

We consider a system of two iso-spectral bosonic modes coupled with a single two-level systems i.e., a qubit. The dynamics is described by a mode-symmetric two-modes Jaynes-Cummings. The entanglement, induced between the two bosonic modes, is analyzed and quantified by negativity. We computed the time evolution of negativity starting from an initial thermal state of the bosonic sector for both zero and finite temperature. We also studied the entangling power of the interaction as a function of mode-qubit detuning and its resilience against temperature increase. Finally a two-qubit gates based on bosonic virtual subsystem is discussed.

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arXiv2005

Quantum entanglement in states generated by bilocal group algebras

Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy for a bipartition (A,B) of a quantum system and conditions to saturate it. We show that these states can be interpreted as ground states of generic Hamiltonians or as the physical states in a quantum gauge theory and that under specific conditions their geometric entropy satisfies the entropic area law. If G is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (i.e., bipartite) graph states and they include GHZ, cluster states etc. Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states.

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arXiv2005

Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems

Entanglement of the ground states in $XXZ$ and dimerized Heisenberg spin chains as well as in a two-leg spin ladder is analyzed by using the spin-spin concurrence and the entanglement entropy between a selected sublattice of spins and the rest of the system. In particular, we reveal that quantum phase transition points/boundaries may be identified based on the analysis on the local extreme of this entanglement entropy, which is illustrated to be superior over the concurrence scenario and may enable us to explore quantum phase transitions in many other systems including higher dimensional ones.

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