Dynamic structure factor in impurity-doped spin chains

Bohrdt, Annabelle; Jägering, Kevin; Eggert, Sebastian; Schneider, I.

doi:10.1103/physrevb.98.020402

Cited by 8 publications

(6 citation statements)

References 77 publications

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“…4, or more explicitly Fig. 9 in which this term is plotted as a function of the boundary magnetic field h), so that the deviation is exponentially decreasing in L in this regime, as expected 7 . Moreover, we see from (4.50) that there are two possible choices ± for the deviation , corresponding to the two possible choices of the sign in (4.50).…”

Section: The Ground State Degeneracy At H + = H −supporting

confidence: 71%

“…While the bulk physics of spin chains can be usually studied by considering the large-size limit of systems with periodic boundary conditions, a richer phenomenology can be observed in the presence of open boundaries, as for example in doped spin chains [7][8][9]. By tuning different parameters at the boundaries one can explore different phase transitions (also experimentally [10]), as well as probing the existence of boundary modes.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Note that, in the case of the ground state that we consider here, the set of complex roots is either empty or equal to α N , and the number n of holes is either 0 or 1. It is easy to solve (5.5) at leading order in L, by noticing that the function p can be obtained as 7) in terms of the derivative ρ of the function (4.8), see (4.7). Therefore, the u solving (5.5) is of the form…”

Section: (53)mentioning

confidence: 99%

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Open XXZ chain and boundary modes at zero temperature

2019

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We study the open XXZ spin chain in the anti-ferromagnetic regime and for generic longitudinal magnetic fields at the two boundaries. We discuss the ground state via the Bethe ansatz and we show that, for a chain of even length L and in a regime where both boundary magnetic fields are equal and bounded by a critical field, the spectrum is gapped and the ground state is doubly degenerate up to exponentially small corrections in L. We connect this degeneracy to the presence of a boundary root, namely an excitation localized at one of the two boundaries. We compute the local magnetization at the left edge of the chain and we show that, due to the existence of a boundary root, this depends also on the value of the field at the opposite edge, even in the half-infinite chain limit. Moreover we give an exact expression for the large time limit of the spin autocorrelation at the boundary, which we explicitly compute in terms of the form factor between the two quasi-degenerate ground states. This, as we show, turns out to be equal to the contribution of the boundary root to the local magnetization. We finally discuss the case of chains of odd length.

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Section: The Ground State Degeneracy At H + = H −supporting

confidence: 71%

Section: Introduction and Main Resultsmentioning

confidence: 99%

Section: (53)mentioning

confidence: 99%

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Open XXZ chain and boundary modes at zero temperature

2019

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“…There has been a resurgence of interest on the effects of impurities in spin-1/2 Heisenberg chains recently due to experimental realizations in solid state systems and in particular in ultracold gases [1]. The impurities effectively can display as missing sites or couplings, which give rise to isolated finite chain segments, that attain characteristic boundary correlation functions, † Deceased.…”

Section: Introductionmentioning

confidence: 99%

“…which would lead to impurity-induced changes in the Knight shift, the susceptibility, the static structure factor, and the ordering temperature [1].…”

Section: Introductionmentioning

confidence: 99%

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Weiss,

Massih

2022

Preprint

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Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson-Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1 ≤ c ≤ 0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration c p . The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

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Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Weiss

Massih²

2022

Annals of Physics

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Dynamic structure factor in impurity-doped spin chains

Cited by 8 publications

References 77 publications

Open XXZ chain and boundary modes at zero temperature

Open XXZ chain and boundary modes at zero temperature

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

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