arXiv subjects

Germán Sierra

Publications and source records attributed to Germán Sierra.

At least 37 records · Page 2Linked to original sources

arXiv2022

Algebraic Bethe Circuits

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary $R$ matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-$\frac{1}{2}$ XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on $4$ sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

quant-ph↗

arXiv2022

Exotic correlation spread in free-fermionic states with initial patterns

We describe a relation between the light-cone velocities after a quantum quench and the internal structure of the initial state, in the particular case of free fermions on a chain at half filling. The considered states include short-range valence bond solids, i.e., dimerized states, and long-range states such as the rainbow. In all the considered cases the correlations spread into one or a few well-defined light cones, each of them presenting an effective velocity which can be read from the form factor. Interestingly, we find that the observed velocities range from zero to the Fermi velocity and may not always be obtained from the dispersion relation for valid momenta.

quant-ph↗

arXiv2022

Simulating violation of causality using a topological phase transition

We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1] known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state (GS) of the model can be related to the optimal strategy of the causal order game. Subsequently, we observe that at the point of maximum violation of the classical bound in the causal order game, corresponding quantum many-body model undergoes a second-order quantum phase transition (QPT). The correspondence equally holds even when we generalize the game for a higher number of parties.

quant-ph↗

arXiv2021

Entanglement in non-critical inhomogeneous quantum chains

We study an inhomogeneous critical Ising chain in a transverse field whose couplings decay exponentially from the center. In the strong inhomogeneity limit we apply Fisher's renormalization group to show that the ground state is formed by concentric singlets similar to those of the rainbow state of the XX model. In the weak inhomogeneity limit we map the model to a massless Majorana fermion living in a hyperbolic spacetime, where, using CFT techniques, we derive the entanglement entropy that is violated linearly. We also study an inhomogeneous non-critical Ising model that for weak inhomogeneity is mapped to a massive Majorana fermion, while for strong inhomogeneity regime it exhibits trivial and non-trivial topological phases and a separation between regions with high and low entanglement. We also present the entanglement Hamiltonian of the model.

cond-mat.str-el↗

arXiv2021

Platonic Entanglement

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.

quant-ph↗

arXiv2021

Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian

The Haldane phase is the prototype of symmetry protected topological (SPT) phases of spin chain systems. It can be protected by several symmetries having in common the degeneracy of the entanglement spectrum. Here we explore in depth this degeneracy for the spin-1 AKLT and bilinear-biquadratic Hamiltonians and show the emergence of a bulk-edge correspondence that relates the low energy properties of the entanglement Hamiltonian of a periodic chain and that of the physical Hamiltonian of an open chain. We find that the entanglement spectrum can be described in terms of two spins-1/2 behaving as the effective spins at the end of the open chain. In the case of non-contiguous partitions, we find that the entanglement Hamiltonian is given by the spin-1/2 Heisenberg Hamiltonian, which suggests a relationship between SPT phases and conformal field theory. We finally investigate the string order parameter and the relation with the bulk-edge correspondence.

quant-ph↗

arXiv2021

Emergent geometry from entanglement structure

We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a generalized adjacency matrix. We show this representation is often exact and may lead to a geometry very different than suggested by the Hamiltonian. Moreover, in all the cases, it yields a natural entanglement contour, similar to previous proposals. The formalism is extended for conformal invariant systems, and a more insightful interpretation of entanglement is presented as a flow among different parts of the system.

quant-ph↗

arXiv2021

Simulating quench dynamics on a digital quantum computer with data-driven error mitigation

Error mitigation is likely to be key in obtaining near term quantum advantage. In this work we present one of the first implementations of several Clifford data regression based methods which are used to mitigate the effect of noise in real quantum data. We explore the dynamics of the 1-D Ising model with transverse and longitudinal magnetic fields, highlighting signatures of confinement. We find in general Clifford data regression based techniques are advantageous in comparison with zero-noise extrapolation and obtain quantitative agreement with exact results for systems of 9 qubits with circuit depths of up to 176, involving hundreds of CNOT gates. This is the largest systems investigated so far in a study of this type. We also investigate the two-point correlation function and find the effect of noise on this more complicated observable can be mitigated using Clifford quantum circuit data highlighting the utility of these methods.

quant-ph↗

arXiv2021

Link representation of the entanglement entropies for all bipartitions

We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry associated with the entanglement structure of a quantum many-body state which may occasionally differ from the one suggested by the Hamiltonian of the system. Yet, the obtention of these entanglement links is a complex mathematical problem. In this work, we address this issue and propose several approximation techniques for matrix product states, free fermionic states, or in cases in which contiguous blocks are specially relevant. Along with this, we discuss the accuracy of the approximation for different types of states and partitions. Finally, we employ the link representation to discuss two different physical systems: the spin-1/2 long-range XXZ chain and the spin-1 bilinear biquadratic chain.

quant-ph↗

arXiv2020

Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

This work concerns Ising quasiholes in Moore-Read type lattice wave functions derived from conformal field theory. We commence with constructing Moore-Read type lattice states and then add quasiholes to them. By use of Metropolis Monte Carlo simulations, we analyze the features of the quasiholes, such as their size, shape, charge, and braiding properties. The braiding properties, which turn out to be the same as in the continuum Moore-Read state, demonstrate the topological attributes of the Moore-Read lattice states in a direct way. We also derive parent Hamiltonians for which the states with quasiholes included are ground states. One advantage of these Hamiltonians lies therein that we can now braid the quasiholes just by changing the coupling strengths in the Hamiltonian since the Hamiltonian is a function of the positions of the quasiholes. The methodology exploited in this article can also be used to construct other kinds of lattice fractional quantum Hall models containing quasiholes, for example investigation of Fibonacci quasiholes in lattice Read-Rezayi states.

cond-mat.str-el↗

arXiv2020

Entanglement as geometry and flow

We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all $2^N$ bipartitions of an $N$-party pure quantum system by means of a (generalized) adjacency matrix. In the cases where the representation is exact, the elements of that matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all the cases it yields a natural {\em entanglement contour} which is similar to previous proposals.Moreover, for one-dimensional conformal invariant systems, the generalized adjacency matrix is given by the two-point correlator of an {\em entanglement current} operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.

quant-ph↗

arXiv2020

Field Tensor Network States

We define a class of tensor network states for spin systems where the individual tensors are functionals of fields. The construction is based on the path integral representation of correlators of operators in quantum field theory. These tensor network states are infinite dimensional versions of matrix product states and projected entangled pair states. We find the field-tensor that generates the Haldane-Shastry wave function and extend it to two dimensions. We give evidence that the latter underlies the topological chiral state described by the Kalmeyer-Laughlin wave function.

cond-mat.stat-mech↗

arXiv2019

Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect

The {\em rainbow state} denotes a set of valence bond states organized concentrically around the center of a spin 1/2 chain. It is the ground state of an inhomogeneous XX Hamiltonian and presents maximal violation of the area law of entanglement entropy. Here, we add a tunable exchange coupling constant at the center, $γ$, and show that it induces entanglement transitions of the ground state. At very strong inhomogeneity, the rainbow state survives for $0 \leq γ\leq 1$, while outside that region the ground state is a product of dimers. In the weak inhomogeneity regime the entanglement entropy satisfies a volume law, derived from CFT in curved spacetime, with an effective central charge that depends on the inhomogeneity parameter and $γ$. In all regimes we have found that the entanglement properties are invariant under the transformation $γ\longleftrightarrow 1 - γ$, whose fixed point $γ= \frac{1}{2}$ corresponds to the usual rainbow model. Finally, we study the robustness of non trivial topological phases in the presence of the defect.

cond-mat.str-el↗

arXiv2019

The Riemann zeros as spectrum and the Riemann hypothesis

We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The corresponding Hamiltonian admits a self-adjoint extension that is tuned to the phase of the zeta function, on the critical line, in order to obtain the Riemann zeros as bound states. The model suggests a proof of the Riemann hypothesis in the limit where the potentials vanish. Finally, we propose an interferometer that may yield an experimental observation of the Riemann zeros.

math-ph↗

arXiv2018

Breaking the Area Law: The Rainbow State

An exponential deformation of a 1D critical Hamiltonian, with couplings falling on a length scale $h^{-1}$, gives rise to ground states whose entanglement entropy follows a volume law, i.e. the area law is violated maximally. The ground state is now in the so-called {\em rainbow phase}, where valence bonds connect sites on the left half with their symmetric counterparts on the right. Here we discuss some of the most relevant features of this rainbow phase, focusing on the XX and Heisenberg models. Moreover, we show that the rainbow state can be understood either as a thermo-field double of a conformal field theory with a temperature proportional to $h$ or as a massless Dirac fermion in a curved spacetime with constant negative curvature proportional to $h$. Finally, we introduce a study of the time-evolution of the rainbow state after a quench to a homogeneous Hamiltonian.

quant-ph↗

arXiv2018

Symmetry protected phases in inhomogeneous spin chains

It has been shown recently that inhomogenous spin chains can exhibit exotic phenomena such as the breaking of the area law of the entanglement entropy. An example is given by the rainbow model where the exchange coupling constants decrease from the center of the chain. Here we show that by folding the chain around its center, the long-range entanglement becomes short-range which can lead to topological phases protected by symmetries (SPT). The phases are trivial for bond-centered foldings, and non trivial for site-centered ones. In the latter case, the folded spin 1/2 chain with $U(1)$ symmetry belongs to the Su-Schrieffer-Heeger class, while the folded chain with $SU(2)$ symmetry is in the Haldane phase. Finally, we extend these results to higher spin chains where we find a correspondence between the symmetry protection of gapped and gapless phases.

cond-mat.str-el↗

arXiv2018

Bosonic Gaussian states from conformal field theory

We study nonchiral wave functions for systems with continuous spins obtained from the conformal field theory (CFT) of a free, massless boson. In contrast to the case of discrete spins, these can be treated as bosonic Gaussian states, which allows us to efficiently compute correlations and entanglement properties both in one (1D) and in two spatial dimensions (2D). In 1D, the computed entanglement entropy and spectra are in agreement with the underlying CFT. Furthermore, we construct a 1D parent Hamiltonian with a low-energy spectrum corresponding to that of a free, massless boson. In 2D, we find edge excitations in the entanglement spectrum, although the states do not have intrinsic topological order, as revealed by a determination of the topological entanglement entropy.

cond-mat.str-el↗

arXiv2018

Effective description of correlations for states obtained from conformal field theory

We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for XXZ spin chains and they are similar to lattice Laughlin states in two dimensions. We show that their zz correlations are determined by a modification of the original free-boson theory. An expansion to quadratic order leads to a solvable, effective theory for the correlations in these states. Compared to the massless boson, there is an additional term in this effective theory that explains the behavior of the correlations: a polynomial decay in one dimension and at the edge of a two-dimensional system and an exponential decay in the bulk of a two-dimensional system. We test the validity of our approximation by comparing it to Monte Carlo computations.

cond-mat.str-el↗