The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasi-particles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional $S=1/2$ Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the non-local nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed matter physics. Here we show theoretically that \emph{quench spectroscopy} for synthetic quantum matter -- which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions -- can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure non-local spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on new exact results for the quench dynamics of quantum spin chains; and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasi-particles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional $S=1/2$ Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the non-local nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed matter physics. Here we show theoretically that \emph{quench spectroscopy} for synthetic quantum matter -- which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions -- can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure non-local spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on new exact results for the quench dynamics of quantum spin chains; and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.

arXiv:2407.14802Jul 20, 20240 citations

Entanglement in Spin Chains

K. Sengupta

arXiv:2109.02657Quantum science and technologyJan 1, 202232 citations

Entanglement in fermionic systems

Bei Zeng

Jan 1, 20120 citations

Exotic Kondo effect in two one-dimensional spin-1/2 chains coupled to two localized spin-1/2 magnets

Igor Kuzmenko, Tetyana Kuzmenko, Y. B. Band +1 more

We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by α=u,d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan–Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain “spins” via the Kondo effect. We calculate the Kondo temperature TK and derive the temperature dependence of the entropy, the specific heat and the “magnetic susceptibility” of the dot for T≫TK. Our results can be generalized to the case of antiferromagnetic XX chains.We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by α=u,d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan–Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain “spins” via the Kondo effect. We calculate the Kondo temperature TK and derive the temperature dependence of the entropy, the specific heat and the “magnetic susceptibility” of the dot for T≫TK. Our results can be generalized to the case of antiferromagnetic XX chains.

arXiv:2408.04353Low Temperature PhysicsDec 1, 20240 citations

Complete characterization of spin chains with two Ising symmetries

Bat-el Friedman, Atanu Rajak, Emanuele G. Dalla Torre

Spin chains with two Ising symmetries are the Jordan-Wigner duals of one-dimensional interacting fermions with particle-hole and time-reversal symmetry. From earlier works on Majorana chains, it is known that this class of models has 10 distinct topological phases. In this paper, we analyze the physical properties of the correspondent 10 phases of the spin model. In particular, thanks to a set of two non-commuting dualities, we determine the local and non-local order parameters of the phases. We find that 4 phases are topologically protected by the Ising symmetries, while the other 6 break at least one symmetry. Our study highlights the non-trivial relation between the topological classifications of interacting bosons and fermions.Spin chains with two Ising symmetries are the Jordan-Wigner duals of one-dimensional interacting fermions with particle-hole and time-reversal symmetry. From earlier works on Majorana chains, it is known that this class of models has 10 distinct topological phases. In this paper, we analyze the physical properties of the correspondent 10 phases of the spin model. In particular, thanks to a set of two non-commuting dualities, we determine the local and non-local order parameters of the phases. We find that 4 phases are topologically protected by the Ising symmetries, while the other 6 break at least one symmetry. Our study highlights the non-trivial relation between the topological classifications of interacting bosons and fermions.

arXiv:1708.03400Europhysics Letters (EPL)Feb 4, 20193 citations

Entanglement in a quantum mixed-spin chain

Xiang Hao, Shiqun Zhu

arXiv:quant-ph/0605063Physics Letters AFeb 10, 200719 citations

S=1/2

Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the non-local nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed matter physics. Here we show theoretically that \emph{quench spectroscopy} for synthetic quantum matter -- which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions -- can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure non-local spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on new exact results for the quench dynamics of quantum spin chains; and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.