The structure of operators in effective particle-conserving models

Knetter, Christian; Schmidt, K. P.; Uhrig, Götz S.

doi:10.1088/0305-4470/36/29/302

Cited by 127 publications

(226 citation statements)

References 29 publications

(100 reference statements)

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“…The results for the Mott phase are obtained for commensurate filling n = 1. For fillings n = 1 the reference state used for normal ordering before truncation should ideally be the disordered state at the lower filling n [7,26]. This requires to redo the whole CUT for each n. But the effect of a different reference state is not very large if t/U is small.…”

Section: Resultsmentioning

confidence: 99%

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

2006

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In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.

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Section: Resultsmentioning

confidence: 99%

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

2006

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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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“…The original Hamiltonian H can be replaced with an effective one H eff which conserves the number of quasiparticles. The Hamiltonian H eff is obtained by continuous unitary transformation; that is, H eff = H(∞) (satisfying [H(∞), Q] = 0) 12,13 . Because of the conservation relation, one can rewrite…”

Section: Perturbative Continuous Unitary Transformation (Pcut)mentioning

confidence: 99%

“…(4) keeps only those processes that conserve the number of quasiparticles and eliminates all parts of H changing the number of quasiparticles 12,13 . To obtain a final diagonalized Hamiltonian, the number of energy quanta created or annihilated at ℓ → ∞ must be zero.…”

Section: Perturbative Continuous Unitary Transformation (Pcut)mentioning

confidence: 99%

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

Hemmatiyan

Movassagh

Ghassemi

et al. 2015

J. Phys.: Condens. Matter

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The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the "perturbative continuous unitary transformations" approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.

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The structure of operators in effective particle-conserving models

Cited by 127 publications

References 29 publications

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

Time-dependent correlations in quantum magnets at finite temperature

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

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