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1
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Electron Spectral Functions in the Presence of the Antiferromagnetic Order in the Two-Dimensional Hubbard Model

100%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2010
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vol. 118
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issue 2
267-272
EN
We use a recently proposed quantum SU(2)×U(1) rotor approach for the Hubbard model to calculate electronic spectral functions in a presence of an antiferromagnetic state for any value of the Coulomb interaction. We isolate the collective variables for charge and spin in the form of the space-time fluctuating U(1) phase field and SU(2) rotating spin quantization axis, respectively. As a result, the fermion Green function in the space-time domain becomes a product of a CP^1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. In turn, the spectral lines are obtained by performing the convolution of spin, charge and pseudo-fermion Green's functions. We observe an emergence of a sharp peak in the electron spectral functions within the antiferromagnetic phase, whose spectral weight is equal to the antiferromagnetic order parameter.
2
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Neutral Bosonic Condensates in Layered 2D Structures under Artificial Magnetic Field

100%
Polak T., Zaleski T.
Acta Physica Polonica A
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2012
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vol. 121
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issue 5-6
1312-1314
EN
We show that the properties of the ideal Bose gas in three-dimensional optical lattice can be closely mimicked by finite two dimensional systems with only ten of layers. The match between critical properties strongly depends on the anisotropy of the hopping amplitudes in and between layers which we fully control. The theory we provided can be directly used in the experiments and results in less challenging requirements of the setups. We also present the phase diagram with its non-monotonic dependence of the ratio of tunneling to on-site repulsion when artificial magnetic field is applied to the system.
3
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Phase Diagram of Mixtures of Ultracold Bosons in Optical Lattice

100%
Anufriiev S., Zaleski T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
629-632
EN
We study a behaviour of mixture of two species of ultracold bosons trapped in optical lattice. Using mean-field approximation, we determine the phase diagram of the system for wide range of parameters. We observe that each of the groups of atoms can condense into superfluid state or localize and form the Mott insulator, which yields that the whole system is either superfluid, the Mott insulator, or a mixed state. It appears that introduction of interaction between different kinds of atoms can strongly renormalise the phase diagram. It can alter the critical behaviour modifying multi-criticality of crossing points and order of phase transitions between mixed and superfluid states.
4
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Superconducting Critical Temperature of Homologous Series of High-T_c Cuprates as a Function of Number of Layers

100%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2004
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vol. 106
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issue 5
561-567
EN
We have considered a model of n-layer high-temperature cuprates of homologous series like HgBa_2Ca_{n-1}Cu_nO_{2+2n+δ} to determine the dependence of the critical temperature T_c(n) on the number n of Cu-O planes in an elementary cell. Focusing on the description of the high-temperature superconducting system in terms of the collective phase variables, we have studied a semi-microscopic anisotropic three-dimensional vector XY model of stacked copper-oxide layers with adjustable parameters representing microscopic in-plane and out-of-plane phase stiffnesses. The model captures the layered composition and block structure along c-axis of superconducting homologous series. Implementing the spherical closure relation we have solved the phase XY model exactly with the help of transfer matrix method for vector variables. The calculated dependence of the critical temperature T_c(n) on the block size n is monotonic with n.
5
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Antiferromagnetic Order in the Hubbard Model: Spin-Charge Rotating Reference Frame Approach

100%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2008
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vol. 114
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issue 1
247-251
EN
We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice. We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem. As our theory describes the evolution from a Slater (U ≪ t) to a Mott-Heisenberg (U ≫ t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.
6
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Ultra-Cold Bosons in Optical Lattice: Time-of-Flight Imaging of Atom-Atom Correlations

100%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
796-800
EN
In the present paper, we investigate a system of strongly interacting bosons confined in two-dimensional optical lattice. We propose a combination of the Bogoliubov method with the quantum rotor approach and determine the spatial atom-atom correlations. This allows us to calculate time-of-flight absorption images, which exhibit all the characteristic features present in experimental results, namely transition from superfluid peaks to Mott insulating blob.
7
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The Existence of the 60 K Plateau in the YBa_2Cu_3O_{6+y} Phase Diagram: the Role of Oxygen Ordering and Charge Imbalance

100%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2007
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vol. 111
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issue 5
705-711
EN
We propose a semi-microscopic model of YBa_2Cu_3O_{6+y} to investigate the origin of the 60 K plateau in its phase diagram. Our model is a "phase only" approach to the high-temperature superconducting system in terms of collective variables. It is able to capture characteristic energy scales present in YBa_2Cu_3O_{6+y} by using adjustable parameters representing phase stiffnesses and allows for strong anisotropy within basal planes to simulate oxygen ordering. We solve the model calculated T_c for chosen system parameters investigating the influence of oxygen ordering and doping imbalance on the shape of YBa_2Cu_3O_{6+y} phase diagram. Our results suggest that the oxygen ordering alone does not seem to be responsible for the existence of the 60 K plateau. However, relying on experimental data unveiling that oxygen doping of YBa_2Cu_3O_{6+y} may introduce a significant charge imbalance between CuO_2 planes and other sites, we show that simultaneously the former are underdoped, while the latter - strongly overdoped almost in the whole region of oxygen doping in which YBa_2Cu_3O_{6+y} is superconducting. This provides two natural counter acting factors, which possibly lead to rise the 60 K plateau with increasing oxygen doping.
8
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Dynamic Structure Factor of Ultracold Bosons in Optical Lattice

100%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
564-568
EN
Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems. Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate one- and two-particle excitations, which are a measure of inter-particle correlations. We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems. Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform. We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below T_{c} in cuprates or smeared excitation spectra characteristic for strongly interacting systems.
9
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Optical Conductivity of Ultra-Cold Bosons in Optical Lattices

81%
Grygiel B., Patucha K., Zaleski T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
633-636
EN
We study ultra-cold bosonic systems in optical lattice using quantum rotor approach to calculate the current-current correlations, which provides the information about conductivity of the system. The method allows us to go beyond mean-field approximation and track the behavior of the real part of the conductivity along the phase transition between the Mott insulator and superfluid state for various geometries of the lattice. In the phase-ordered state at zero temperature, a discrete ingredient appears resulting from the long-range coherence in the system.
10
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Role of Bandwidths and Energy Gap in Formation of Ground State of Ultra-Cold Bosons in Artificial Magnetic Fields

81%
Patucha K., Grygiel B., Zaleski T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
637-640
EN
We study the properties of ultra-cold bosons in optical lattice in arbitrary gauge potentials. Using quantum rotor approach we are able to go beyond mean-field approximation thus taking into account subtleties of the band structure of the artificial magnetic field. This allows us to elucidate the interplay of the subbands widths and energy gaps on the formation of the coherent state. As a result, we are able to pinpoint the elements of the band structure, which are crucial to proper theoretical description of the synthetic magnetic field in a lattice bosonic system. This leads us finally to a method of approximation of the Hofstadter butterfly spectrum with a simpler band structure and use it to investigate the ground state of the system for a wide range of magnetic fluxes.
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