Adapted continuous unitary transformation to treat systems with quasi-particles of finite lifetime

Fischer, Tim; Duffe, Sebastian; Uhrig, Götz S.

doi:10.1088/1367-2630/12/3/033048

Cited by 48 publications

(101 citation statements)

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“…Additionally, we keep only terms that create or annihilate at most N = 4 triplons in the Hamiltonian and N = 3 triplons in the observables, see also Ref. [16,43]. them, and α ∈ {x, y, z} the spin polarization.…”

Section: P-1mentioning

confidence: 99%

“…Such systems are of great current interest because they allow for the study of Bose-Einstein condensation of triplons and of the massless excitations above this condensate [8,9]. Additionally, they represent gapped quantum liquids known to display considerable quasiparticle decay [13][14][15][16].…”

Section: P-1mentioning

confidence: 99%

“…Theoretically as well, there is rising interest in the understanding and quantitative description of this phenomenon for gapped triplons [13][14][15][16] as well as for gapless magnons [17][18][19].…”

mentioning

confidence: 99%

“…Diagrammatic approaches are able to capture the qualitative features but may encounter difficulties in the quantitative description in the regime of strong merging where the sharp mode dissolves completely in the continuum because this is a strong coupling phenomenon [13,14]. Unitary transformations also face difficulties when modes of finite life-time occur [16].…”

mentioning

confidence: 99%

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Microscopic model for Bose-Einstein condensation and quasiparticle decay

Fischer¹,

Duffe²,

Uhrig³

2011

EPL

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Abstract. -Sufficiently dimerized quantum antiferromagnets display elementary S = 1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1 ≈ −2.3 meV, J2 ≈ 1.2 meV, J3 ≈ 2.9 meV and J4 ≈ −0.3 meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S = 1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.Low-dimensional antiferromagnetic quantum spin systems display various fascinating properties, e.g., spinPeierls transition [1, 2], appearance of a Haldane gap for integer spins [3,4], high-temperature superconductivity upon doping [5], and the Bose-Einstein condensation (BEC) in spin-dimer systems [6][7][8][9], where the latter one is characterized by a phase transition from a non-magnetic phase to a long-range antiferromagnetically ordered gapless phase at a critical magnetic field H c1 .Another fascinating phenomenon recently observed in low-dimensional antiferromagnets is the decay of their elementary S = 1 excitations, triplons [10], at higher energies so that the triplons exist only in a restricted part of the Brillouin zone [11,12]. Theoretically as well, there is rising interest in the understanding and quantitative description of this phenomenon for gapped triplons [13][14][15][16] as well as for gapless magnons [17][18][19].The description of quasiparticle decay faces an intrinsic difficulty. The merging of the long-lived, infinitely sharp elementary triplon with a multitriplon continuum requires to describe the resulting resonance and its edges precisely. This is still a challenge for numerical approaches such as exact diagonalization or dynamic density-matrix (a) fischer@fkt.physik.tu-dortmund.de (b) goetz.uhrig@tu-dortmund.de renormalization [20]. Diagrammatic approaches are able to capture the qualitative features but may encounter difficulties in the quantitative description in the regime of strong merging where the sharp mode dissolves completely in the continuum because this is a strong coupling phenomenon [13,14]. Unitary transformations also face difficulties when modes of finite life-time occur [16].A crucial step in the understanding of both phenomena is to identify a suitable experimental system. The best studied candidate for the BEC in coupled spin-dimer systems is TlCuCl 3 . Unfortunately, recent research suggests that the high field spectrum remains gapped [21,22] in contrast to what is expected from a phase where a continuous s...

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Section: P-1mentioning

confidence: 99%

Section: P-1mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Microscopic model for Bose-Einstein condensation and quasiparticle decay

Fischer¹,

Duffe²,

Uhrig³

2011

EPL

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“…To capture the zero temperature quantum fluctuations quantitatively we apply a continuous unitary transformation [30][31][32][33][34] that conserves the number of triplons in the system. To first order in the parameter α the effective Hamiltonian is given by…”

Section: Theory: Diagrammatic Brückner Approachmentioning

confidence: 99%

Time-dependent correlations in quantum magnets at finite temperature

et al. 2016

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In this Rapid Communication we investigate the time dependence of the gap mode of copper nitrate at various temperatures. We combine state-of-the-art theoretical calculations with high precision neutron resonance spin-echo measurements to understand the anomalous decoherence effects found previously in this material. It is shown that the time domain offers a complementary view on this phenomenon, which allows us to directly compare experimental data and theoretical predictions without the need of further intensive data analysis, such as (de)convolution.

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Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems

Vanderstraeten

2017

Springer Theses

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Zo hoort de theoretische fysica te zijn, geen verpleeghuis voor kreupelen, maar een speelplaats voor gezonde, vitale, bloeiende, lachende, vrolijke losbollen, welgeschapen, complete wezens die tevreden zijn met zichzelf, die ieder voor zich het ideaalbeeld zijn van hun moeder en de kracht van hun vaders lendenen, niet de misgeboorten van vage wensen, niet de nageboorte die met de naweeën komt. Het onderhavige werk is het resultaat van vier jaar vertoeven op deze speelplaats die theoretische fysica heet, en ik heb het steeds als een voorrecht ervaren aan dit mooie project te mogen meewerken. Dit voorwoord is de ideale plaats om de mensen te bedanken die het mij hebben mogelijk gemaakt om van dit voorrecht te genieten. Eerst en vooral dien ik mijn promotoren-duo te bedanken, die mij op deze ontdekking doorheen de kwantumveeldeeltjesfysica hebben begeleid. Zonder Jutho was ik waarschijnlijk nooit terecht gekomen in deze prachtige wetenschap, en hij heeft zich nooit enige moeite gespaard om mij verder te helpen als ik ergens vastzat. Frank ben ik dankbaar voor zijn vertrouwen, enthousiasme en onafgebroken toevoer van suggesties en ideeën, die mij hebben toegelaten om mijn eigen weg te zoeken doorheen het kwantumdoolhof. Natuurlijk gaat ook mijn dank uit naar alle 'vrolijke losbollen' van de Gentse kwantumgroep:

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Adapted continuous unitary transformation to treat systems with quasi-particles of finite lifetime

Cited by 48 publications

References 77 publications

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Time-dependent correlations in quantum magnets at finite temperature

Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems

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