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Lukasz Cincio

Publications and source records attributed to Lukasz Cincio.

98 records · Page 6Linked to original sources
arXiv2015

Local convertibility of the ground state of the perturbed Toric code

We present analytical and numerical studies of the behaviour of the $α$-Renyi entropies in the Toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC) - a property called local-convertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of $α$ within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

quant-ph↗
arXiv2013

Local response of topological order to an external perturbation

We study the behavior of the Rényi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that Rényi entropies of different index α display derivatives with opposite sign, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, cluster states, and other quantum spin liquids. The fact that the size of the subsystem does not need to scale with the correlation length makes it possible for this effect to be accessed experimentally.

quant-ph↗
arXiv2012

Characterizing topological order by studying the ground states of an infinite cylinder

Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network representation of a complete, orthonormal set of ground states on a cylinder of infinite length and finite width is obtained through numerical optimization. Each of these ground states is argued to have a different anyonic flux threading through the cylinder. In a chiral phase, the entanglement spectrum of each ground state is seen to reveal a different sector of the corresponding gapless edge theory. A quasi-orthogonal basis on the torus is then produced by chopping off and reconnecting the tensor network representation on the cylinder. Elaborating on the recent proposal of [Y. Zhang et al. Phys. Rev. B 85, 235151 (2012)], a rotation on the torus yields an alternative basis of ground states and, through the computation of overlaps between bases, the modular matrices S and U (containing the mutual and self statistics of the different anyon species) are extracted. As an application, we study the hard-core boson Haldane model by using the two-dimensional density matrix renormalization group. A thorough characterization of the universal properties of this lattice model, both in the bulk and at the edge, unambiguously shows that its ground space realizes the ν=1/2 bosonic Laughlin state.

cond-mat.str-el↗
arXiv2010

Spontaneous symmetry breaking in a generalized orbital compass model

We introduce a generalized two-dimensional orbital compass model, which interpolates continuously from the classical Ising model to the orbital compass model with frustrated quantum interactions, and investigate it using the multiscale entanglement renormalization ansatz (MERA). The results demonstrate that increasing frustration of exchange interactions triggers a second order quantum phase transition to a degenerate symmetry broken state which minimizes one of the interactions in the orbital compass model. Using boson expansion within the spin-wave theory we unravel the physical mechanism of the symmetry breaking transition as promoted by weak quantum fluctuations and explain why this transition occurs only surprisingly close to the maximally frustrated interactions of the orbital compass model. The spin waves remain gapful at the critical point, and both the boson expansion and MERA do not find any algebraically decaying spin-spin correlations in the critical ground state.

cond-mat.str-el↗
arXiv2008

Dynamics of a quantum phase transition with decoherence: the quantum Ising chain in a static spin environment

We consider a linear quench from the paramagnetic to ferromagnetic phase in the quantum Ising chain interacting with a static spin environment. Both decoherence from the environment and non-adiabaticity of the evolution near a critical point excite the system from the final ferromagnetic ground state. For weak decoherence and relatively fast quenches the excitation energy, proportional to the number of kinks in the final state, decays like an inverse square root of a quench time, but slow transitions or strong decoherence make it decay in a much slower logarithmic way. We also find that fidelity between the final ferromagnetic ground state and a final state after a quench decays exponentially with a size of a chain, with a decay rate proportional to average density of excited kinks, and a proportionality factor evolving from 1.3 for weak decoherence and fast quenches to approximately 1 for slow transitions or strong decoherence. Simultaneously, correlations between kinks randomly distributed along the chain evolve from a near-crystalline anti-bunching to a Poissonian distribution of kinks in a number of isolated Anderson localization centers randomly scattered along the chain.

quant-ph↗
arXiv2008

Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model

We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising model on the $8\times8$ square lattice are found to be very accurate even with the smallest non-trivial truncation parameter.

cond-mat.other↗
arXiv2007

Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model

Quantum Ising model in one dimension is an exactly solvable example of a quantum phase transition. We investigate its behavior during a quench from a paramagnetic to ferromagnetic phase caused by a gradual turning off of the transverse field at a fixed rate characterized by the quench time $τ_Q$. In agreement with Kibble-Zurek mechanism, quantum state of the system after the transition exhibits a characteristic correlation length $\hatξ$ proportional to the square root of the quench time $τ_Q$. The inverse of this correlation length determines average density of defects after the transition. In this paper, we show that $\hatξ$ also controls the entropy of entanglement of a block of $L$ spins with the rest of the system. For large $L$, this entropy saturates at $\frac16\log_2\hatξ$, as might have been expected from the Kibble-Zurek mechanism. Close to the critical point, the entropy saturates when the block size $L\approx\hatξ$, but -- in the subsequent evolution in the ferromagnetic phase -- a somewhat larger length scale $l=\sqrt{τ_Q}\lnτ_Q$ develops as a result of quantum dephasing, and the entropy saturates when $L\approx l$. We also study the spin-spin correlation. We find that close to the critical point ferromagnetic correlations decay exponentially with the dynamical correlation length $\hatξ$, but in the following evolution this correlation function becomes oscillatory at distances less than this scale. However, both the wavelength and the correlation length of these oscillations are still determined by $\hatξ$. We also derive probability distribution for the number of kinks in a finite spin chain after the transition.

cond-mat.str-el↗