The new class of exactly solvable models of one-dimensional spin chains is found. Interactions of spins with crystalline electric fields (CEF) and spin-spin coupling between neighboring sites are taken into account for those models. Spin-spin coupling includes higher-order spin operators (the Stevens operators) and describes the interaction between z th components of the spins. We show that essential parts of the Hamiltonians of these models can be written in terms of exactly solvable transverse field Ising model (TFIM), in which certain combinations of the parameters of spin-spin interactions play the role of the TFIM exchange constant, and components of the CEFs play the role of external transverse magnetic field of the TFIM. The obtained results are valid for any values of spin (or total moments for rare-earth ions) and for the wide class of CEFs. The requirement for the exact solvability is that the space of single spin states should be split by the CEF into the subspaces with dimensions ≤ 2 (i.e., the only singlets and doublets are allowed). Cases of integer and half-integer spins are considered. For finite-size chains with integer spins and open ends we show numerically that energy spectra always contain the states whose energies do not depend on the CEF (the magnetic field for the TFIM). The energies (per spin) of these states decay as L − 1 , where L is the chain length. This behavior qualitatively distinguishes these states from known Majorana edge states and strong zero modes, where the energy decreases exponentially in L .The new class of exactly solvable models of one-dimensional spin chains is found. Interactions of spins with crystalline electric fields (CEF) and spin-spin coupling between neighboring sites are taken into account for those models. Spin-spin coupling includes higher-order spin operators (the Stevens operators) and describes the interaction between z th components of the spins. We show that essential parts of the Hamiltonians of these models can be written in terms of exactly solvable transverse field Ising model (TFIM), in which certain combinations of the parameters of spin-spin interactions play the role of the TFIM exchange constant, and components of the CEFs play the role of external transverse magnetic field of the TFIM. The obtained results are valid for any values of spin (or total moments for rare-earth ions) and for the wide class of CEFs. The requirement for the exact solvability is that the space of single spin states should be split by the CEF into the subspaces with dimensions ≤ 2 (i.e., the only singlets and doublets are allowed). Cases of integer and half-integer spins are considered. For finite-size chains with integer spins and open ends we show numerically that energy spectra always contain the states whose energies do not depend on the CEF (the magnetic field for the TFIM). The energies (per spin) of these states decay as L − 1 , where L is the chain length. This behavior qualitatively distinguishes these states from known Majorana edge states and strong zero modes, where the energy decreases exponentially in L .

Physical review. B./Physical review. BJun 9, 20250 citations

Exactly solvable 1D frustrated quantum spin models

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

Zeitschrift für Physik B Condensed MatterJun 1, 19969 citations

Exactly solvable models of spin liquids with spinons, and of three-dimensional topological paramagnets

Daniel Ben-Zion, Diptarka Das, John McGreevy

We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact ``decorated-string-net'' framework to construct several classes of interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions on any bipartite graph. Another example, in any dimension, has ${\mathbb{Z}}_{2}$ topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact ``decorated-string-net'' framework to construct several classes of interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions on any bipartite graph. Another example, in any dimension, has ${\mathbb{Z}}_{2}$ topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.

arXiv:1511.01539Physical review. B./Physical review. BApr 25, 201614 citations

Exact analysis of one-dimensional quantum spin models

康広藤井

Jan 1, 20010 citations

Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model

Masaya Nakagawa, Norio Kawakami, Masahito Ueda

A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.

arXiv:2003.14202Physical Review LettersMar 18, 2021129 citations

{\mathbb{Z}}_{2}

topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.