Trionic phase of ultracold fermions in an optical lattice: A variational study

To investigate ultracold fermionic atoms of three internal states (colors) in an optical lattice, subject to strong attractive interaction, we study the attractive three-color Hubbard model in infinite dimensions by using a variational approach. We find a quantum phase transition between a weak-coupling superconducting phase and a strong-coupling trionic phase where groups of three atoms are bound to a composite fermion. We show how the Gutzwiller variational theory can be reformulated in terms of an effective field theory with three-body interactions and how this effective field theory can be solved exactly in infinite dimensions by using the methods of dynamical mean field theory.Comment: 14 PRB pages, 8 figure

Color Superfluidity and "Baryon" Formation in Ultracold Fermions

We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U| < |U_C|, a color superfluid state emerges with a tendency to domain formation. For |U| > |U_C|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.Comment: 4 PRL pages, 1 figur

Elektron-elektron kölcsönhatás szilárdtestekben - DFG - IRTG = Electron- Electron Interactions in Solids - DFG - IRTG

A kutatási támogatást a Budapest-Marburg nemzetközi doktori iskola két magyar PhD hallgatójának ösztöndíjára fordítottuk. A hallgatók személye a futamidő alatt tanévenként változott, így a beszámolásköteles tevékenység a doktori iskola több témáját is érinti. A ''Nemkonvencionális sűrűséghullámok'' című kutatási irány keretén belül elméleti eredményeinket kísérletekkel összevetve meggyőzően demonstráltuk számos anyag (pl. egyes magashőmérsékletű szupravezetők) esetében, hogy anomális viselkedésük (pszeudogap, termomágneses transzport) hátterében a fázisdiagrammjuk egyes tartományaiban megjelenő nemkonvencionális kondenzátum áll. A ""Kvantum fázisátalakulások erősen korrelált rendszerekben"" című kutatási program keretében kidolgoztuk a trion-szuperfolyadék fázisátmenet elméletét, mely a csapdázott alkáli atomok mellett releváns lehet a hadron-színszupravezető átmenet értelmezése során is. Az ''Elektron spin rezonancia szilárdtestekben'' című témakörben megállapítottuk egy erősen aluldópolt magashőmérsékletű szupravezető ötvözetről, hogy antiferromágneses fázisában a lyuk koncentráció térben inhomogén, és a polarizáció négyforgású szimmetriával rendelkezik. Végezetül a ""Mágneses momentumok frusztrált rácsokon"" című témakörben megvizsgáltuk egy kooperatív paramágnes alacsony energiás modelljét, és meghatároztuk a rendszer fázisdiagrammját, mely rendezett és rendezetlen tartományokkal is rendelkezik. | The grant support was used to finance the fellowships of two hungarian PhD students of the Budapest-Marburg international graduate school. During the grant period the persons supported by the fellowships changed from schoolyear to schoolyear, therefore the present report touches upon several projects of the graduate school. While working on the project ''Unconventional density waves'', we compared our theoretical results with experiments, and convincingly demonstrated that a number of materials (e.g. certain high temperature superconductors) owe their anomalous behavior (pseudogap, thermomagnetic transport) to unconventional condensates in regions of their phase diagrams. Work on the project ""Quantum phase transitions in strongly correlated systems"" led to the theory of the trion-superfluid phase transition, which is relevant not only to the understanding of trapped alkali atoms, but to the hadron-colorsuperconductor transition as well. Within the framework of the project ''Electron spin resonance in solids'' we have investigated a strongly underdoped high temperature superconductor compound, and determined that in its antiferromagnetic phase the hole concentration is inhomogeneous, and that the polarization has fourfold symmetry. Finally, in the project ""Magnetic moments on frustrated lattices"" we investigated the low energy model of a cooperative paramagnet, and determined the phase diagram of the system, containing both ordered and disordered regions

Dynamical correlations and quantum phase transition in the quantum Potts model

We present a detailed study of the finite temperature dynamical properties of the quantum Potts model in one dimension.Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix {\gf deep} in the gapped phases is shown to take a simple {\gf exchange} form in the perturbative regimes. The finite temperature correlation functions in the quantum critical regime are determined using conformal invariance, while {\gf far from the quantum critical point} we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [K. Damle and S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay functions exhibit a {\em diffusive character}. {\gf We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition.} Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.Comment: 18 PRB pages added correction

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two- particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice