Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets

Bostrem, I. G.; Овчинников, А. С.; Sinitsyn, Valentine E.

doi:10.3390/sym2020722

Cited by 3 publications

(3 citation statements)

References 73 publications

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“…We can write down the three eigenvalues of Ĥqt for each of the three cases successfully solved with the help of the test roots (32):…”

Section: Eigenvalues Of ĥQt (And Of ĥAs )mentioning

confidence: 99%

“…The systematic search for symmetries and constants of motion exhibited by the Hamiltonian model is reported in Section 3 . A similar route has recently been used to investigate the dynamics of a pair [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ] or a chain [ 32 , 33 ] of coupled spins (also greater than

) subjected to time-independent and time-dependent [ 34 , 35 , 36 ] external magnetic fields. Symmetry arguments have also been exploited to elegantly bring to light intriguing dynamic features of physical systems living in Hilbert spaces of infinite dimensions [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 ].…”

Section: Introductionmentioning

confidence: 99%

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Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Belousov

Man’ko

Migliore

et al. 2022

Entropy

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We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.

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“…We can write down the three eigenvalues of Ĥqt for each of the three cases successfully solved with the help of the test roots (32):…”

Section: Eigenvalues Of ĥQt (And Of ĥAs )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Belousov

Man’ko

Migliore

et al. 2022

Entropy

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show abstract

“…Due to impractical implementations, the total SU(2) spin symmetry of the Heisenberg model is usually not used in numerical approaches [39,97], except the work from Flocke and Karwowski [11,[98][99][100][101][102] using the symmetric group approach (SGA) [103][104][105][106][107], spin-symmetry adapted MPS/DMRG studies [108][109][110][111][112][113][114][115][116] and occasional ED [97,117,118] and real-space renormalization group studies [119]. Nevertheless the theoretical advantages of using a description conserving both total spin projection, m s , the total spin, S, are striking: (a) further reduction of the Hilbert space size (by additional block diagonalization of Ĥ), (b) optimization of electronic states of desired spin, and (c) separation of nearly degenerate states of different total spin.…”

Section: The Heisenberg Modelmentioning

confidence: 99%

Combined unitary and symmetric group approach applied to low-dimensional spin systems

Dobrautz,

Katukuri,

Bogdanov

et al. 2021

Preprint

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A novel combined unitary and symmetric group approach is used to study the spin-1 2 Heisenberg model and related Fermionic systems in a spin-adapted representation, using a linearlyparameterised Ansatz for the many-body wave function. We show that a more compact ground state wave function representation is obtained when combining the symmetric group, Sn, in the form of permutations of the underlying lattice site ordering, with the cumulative spin-coupling based on the unitary group, U(n). In one-dimensional systems the observed compression of the wave function is reminiscent of block-spin renormalization group approaches, and allows us to study larger lattices (here taken up to 80 sites) with the spin-adapted full configuration interaction quantum Monte Carlo method, which benefits from the sparsity of the Hamiltonian matrix and the corresponding sampled eigenstates that emerge from the reordering. We find that in an optimal lattice ordering the configuration state function with highest weight already captures with high accuracy the spin-spin correlation function of the exact ground state wave function. This feature is found for more general lattice models, such as the Hubbard model, and ab initio quantum chemical models, in this work exemplified by a one-dimensional hydrogen chain. We also provide numerical evidence that the optimal lattice ordering for the unitary group approach is not generally equivalent to the optimal ordering obtained for methods based on matrix-product states, such as the density-matrix renormalization group approach.

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Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems

et al. 2022

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Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets

Cited by 3 publications

References 73 publications

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Combined unitary and symmetric group approach applied to low-dimensional spin systems

Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems

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