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arXiv:2112.15512 · Physica Scripta

Understanding the propagation of excitations in quantum spin chains with different kind of interactions

Alejandro Ferrón, Pablo Serra, Omar Osenda

Published Sep 27, 2022• 9 citations
arXivHTMLPDF

Abstract

Abstract The dynamical behavior of the quantum state of different quantum spin chains, with designed site-dependent interaction strengths, is analyzed when the initial state belongs to the one excitation subspace. Our results show that the inhomogeneous chains transfer single excitations with near-perfect fidelity for two different spin chain Hamiltonians. The first one is the ferromagnetic Heisenberg Hamiltonian with nearest neighbor interactions. The second spin chain has long-range anisotropic interactions, ferromagnetic in one direction and antiferromagnetic in the orthogonal plane. Both designed chains have in common a partially ordered spectrum and well-localized eigenvectors. This physical trait unifies the description of both kinds of systems.

DOI
10.1088/1402-4896/ac955c

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We investigate the quality of quantum state transfer through a uniformly coupled antiferromagnetic spin chain in a multiexcitation subspace. The fidelity of state transfer using multiexcitation channels is found to compare well with communication protocols based on the ground state of a spin chain with ferromagnetic interactions. Our numerical results support the conjecture that the fidelity of state transfer through a multiexcitation subspace only depends on the number of initial excitations present in the chain and is independent of the excitation ordering. Based on these results, we describe a communication scheme which requires little effort for preparation.
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-12\frac{1}{2}21​ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XXXXXX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.
We study the magnetic properties of two types of one-dimensional XXXXXX spin-12\frac{1}{2}21​ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.
Abstract Designing a good transfer channel for arbitrary quantum states in spin chains implies optimising a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles the state prepared at the beginning of the transfer protocol. When averaged over all the possible initial states, the figure of merit quantifies the quality of the protocol. There are proposals for optimising a given Hamiltonian to accomplish a particular task. The transfer of quantum states is one of them. In particular, we consider the design of Heisenberg spin chains using a genetic algorithm. This very efficient algorithm allows us to study different properties of Hamiltonians with good to excellent transfer ability. Using an evolutionary population method results in exchange coefficient strengths that change abruptly from site to site, which could hinder implementing an actual physical system with such exchange coefficients. By modifying the cost function, we obtain Hamiltonians with exchange coefficients varying smoothly along the chain length without compromising their transfer ability concerning the rough ones. Besides, both kinds of chain Hamiltonians show similar robustness against static disorder. By studying the statistical properties of the eigenvalues of Hamiltonians with varying transfer abilities, we determine the ensemble of random matrices to which the spectra belong.
The excitation spectrum is studied around the degenerate point at the Ising limit in the one-dimensional anisotropic Heisenberg antiferromagnets with next-nearest-neighbor interactions. Solitons are found as propagation modes in the N\'eel state and in the (2,2) antiphase state, while triplet-dimer excitations are found propagating in the dimer state. These excitations determine the shape of dynamical spin-correlation functions, which are calculated by an exact diagonalization for finite chains. The phase diagram is determined from the condition that the energy gap vanishes in the excitation spectrum.