We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.
Motivated by recent realizations of spin-1 NaRb mixtures in the experiments, here we investigate heteronuclear magnetism in the Mott-insulating regime. Different from the identical mixtures where the boson (fermion) statistics only admits even (odd) parity states from angular momentum composition, for heteronuclear atoms in principle all angular momentum states are allowed, which can give rise to new magnetic phases. Various magnetic phases can be developed over these degenerate spaces, however, the concrete symmetry breaking phases depend not only on the degree of degeneracy, but also the com…
We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the en…
Superconductivity originates from the coupling between charge carriers and bosonic excitations of either phononic or electronic origin. Identifying the most relevant pairing glue is a key step towards a clear understanding of the unconventional superconductivity. Here, by applying the ultrafast optical spectroscopy on the electron-doped cuprates La$_{1.9}$Ce$_{0.1}$CuO$_{4\pmδ}$, we discern a bosonic mode of electronic origin that has the strongest coupling with the charge carriers near $T_c$. We argue that this mode is associated with the two-dimensional antiferromagnetic spin fluctuations, a…
Recent local tunneling data indicate strong nanoscale inhomogeneity of superconducting gap in high temperature superconductors. Strong local nanoscale inhomogeneity in the bosonic scattering mode has also been observed in the same samples. We argue that these two inhomogeneities directly related to each other. To address local boson scattering effects, we develop a local strong coupling model of superconducting pairing in a coarse grained superconducting state. Each patch is characterized by local coupling to the bosonic mode as well as by local mode energy. We find that local gap value on eac…
Electronic band dispersions in copper oxide superconductors have kinks around 70 meV that are typically attributed to coupling of electrons to a bosonic mode. We performed angle resolved photoemission spectroscopy (ARPES) experiments on overdoped cuprate high temperature superconductors to test the relationship between the superconducting transition temperature and electron-bosonic mode coupling. Remarkably, the kinks remain strong in the heavily overdoped region of the doping phase diagram of LSCO, even when the superconductivity completely disappears. This unexpected observation is incompati…
Motivated by experiments on heteronuclear Feshbach resonances in Bose mixtures, we investigate s-wave pairing of two species of bosons in an optical lattice. The zero temperature phase diagram supports a rich array of superfluid and Mott phases and a network of quantum critical points. This topology reveals an underlying structure that is succinctly captured by a two-component Landau theory. Within the second Mott lobe we establish a quantum phase transition described by the paradigmatic longitudinal and transverse field Ising model. This is confirmed by exact diagonalization of the 1D bosonic…
Motivated by the presence of various charge inhomogeneities in strongly correlated systems of coupled ladders, a model of spatially separated bosonic and fermionic degrees of freedom is numerically studied. In this model, bosonic chains are connected to fermionic chains by two types of generalized Andreev couplings. It is shown that for both types of couplings the long-distance pairing correlations are enhanced. Near quarter filling, this effect is much larger for the splitting of a pair in electrons which go to the two neighboring fermionic chains than for a pair hopping process. It is argued…
Competing ferro- and antiferromagnetic exchange interactions may lead to the formation of bound magnon pairs in the high-field phase of a frustrated quantum magnet. With decreasing field, magnon pairs undergo a Bose-condensation prior to the onset of a conventional one-magnon instability. We develop an analytical approach to study the zero-temperature properties of the magnon-pair condensate, which is a bosonic analog of the BCS superconductors. Representation of the condensate wave-function in terms of the coherent bosonic states reveals the spin-nematic symmetry of the ground-state and allow…
Systems showing resonant superfluidity, driven by an exchange coupling of strength $g$ between uncorrelated pairs of itinerant fermions and tightly bound ones, undergo a first order phase transition as $g$ increases beyond some critical value $g_c$. The superfluid phase for $g \leq g_c$ is characterized by a gap in the fermionic single particle spectrum and an acoustic sound-wave like collective mode of the bosonic resonating fermion pairs inside this gap. For $g>g_c$ this state gives way to a phase uncorrelated bosonic liquid with a $q^2$ spectrum.
The present paper makes a connection between collective bosonic states and the exact solutions of the $p_x + ip_y$ pairing Hamiltonian. This makes it possible to investigate the effects of the Pauli principle on the energy spectrum, by gradually reintroducing the Pauli principle. It also introduces an efficient and stable numerical method to probe all the eigenstates of this class of Hamiltonians.
We use exact diagonalization to study the quantum phases and phase transitions when a single species of fermionic atoms at Landau level filling factor $ν_f = 1$ in a rotating trap interact through a p-wave Feshbach resonance. We show that under weak pairing interaction, the system undergoes a second order quantum phase transition from $ν_{f} = 1$ fermionic integer quantum Hall (FIQH) state at positive detuning, to $ν_{b} = \frac{1}{4}$ bosonic fractional quantum Hall (BFQH) state at negative detuning. However, when the pairing interaction increases, a new phase between them emerges, correspond…
Since the discovery of high temperature superconductivity in the iron pnictides and chalcogenides in early 2008, a central issue has been the microscopic origin of the superconducting pairing. Although previous experiments suggest that the pairing may be induced by exchanging the antiferromagnetic spin fluctuations and the superconducting order parameter has opposite signs in the electron and hole pockets as predicted by the S+- pairing model, it remains unclear whether there is a bosonic mode from the tunneling spectrum which has a close and universal relationship with superconductivity as we…
Influence of Harris disorder on quantum-critical superconductivity
Harvard University（哈佛大学）；Episteme, Inc.（Episteme公司）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）
In Part I we discuss accumulating experimental evidence related to the structure and origin of the bosonic spectral function in high-temperature superconducting (HTSC) cuprates at and near optimal doping. Some global properties of the spectral function, such as number and positions of peaks, are extracted by combining optics, neutron scattering, ARPES and tunnelling measurements. These methods give convincing evidence for strong electron-phonon interaction (EPI) with the coupling constant between 1-3 in cuprates near optimal doping. Here we clarify how these results are in favor of the Eliashb…
We explore the Mott insulating state of single-band bosonic pairing Hamiltonians using analytical approaches and large scale density matrix renormalization group calculations. We focus on the second Mott lobe which exhibits a magnetic quantum phase transition in the Ising universality class. We use this feature to discuss the behavior of a range of physical observables within the framework of the 1D quantum Ising model and the strongly anisotropic Heisenberg model. This includes the properties of local expectation values and correlation functions both at and away from criticality. Depending on…
Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, includ…
We consider normal state properties, the pairing instability temperature, and the structure of the pairing gap in electron-doped cuprates. We assume that the pairing is mediated by collective spin excitations, with antiferromagnetism emerging with the appearance of hot spots. We use a low-energy spin-fermion model and Eliashberg theory up to two-loop order. We justify ignoring vertex corrections by extending the model to N >>1 fermionic flavors, with 1/N playing the role of a small Eliashberg parameter. We argue, however, that it is still necessary to solve coupled integral equations for the f…
The phase diagram of LaFeAs$_{1-x}$P$_x$O system has been extensively studied through hole- and electron-doping as well as As/P-substitution. It has been revealed that there are three different superconducting phases with different Fermi surface (FS) topologies and thus with possibly different pairing glues. One of them is well understood as spin fluctuation-mediated superconductivity within a FS nesting scenario. Another one with the FSs in a bad nesting condition must be explained in a different context such as orbital or spin fluctuation in strongly correlated electronic system. In both pha…
Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
Institut Néel, Université Grenoble Alpes and CNRS（内勒研究所，格勒诺布尔阿尔卑斯大学及法国国家科学研究中心）；Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid（凝聚态物理理论系，凝聚态物理中心（IFIMAC）及尼古拉斯·卡布雷拉研究所，马德里自治大学）
We propose a new class of ground states for doped Mott insulators in the electron second-quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the t-J model. At half filling, the ground state describes spin correlations of the S=1/2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exh…
We use bosonization approach to investigate quantum phases in mixtures of bosonic and fermionic atoms confined in one dimensional optical lattices. The phase diagrams can be well understood in terms of polarons, which correspond to atoms that are "dressed" by screening clouds of the other atom species. For a mixture of single species of fermionic and bosonic atoms we find a charge density wave phase, a phase with fermion pairing, and a regime of phase separation. For a mixture of two species of fermionic atoms and one species of bosonic atoms we obtain spin and charge density wave phases, a Wi…
In the description of spin-charge separation based on the phase string theory of the t-J model, spinon excitations are vortices in the superconducting state. Thermally excited spinons destroy phase coherence, leading to a new phase characterized by the presence of free spinon vortices at temperatures, T_c<T<T_v. The temperature scale T_v at which holon condensation occurs marks the onset of pairing amplitude, and is related to the spin pseudogap temperature T^*. The phase below T_v, called the spontaneous vortex phase, shows novel transport properties before phase coherence sets in at T_c. We …
An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a non-zero winding number introduced in A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786. The topological character of the weak pairing phase is protected by a discrete …
We address the quantum-critical behavior of a two-dimensional itinerant ferromagnetic systems described by a spin-fermion model in which fermions interact with close to critical bosonic modes. We consider Heisenberg ferromagnets, Ising ferromagnets, and the Ising nematic transition. Mean-field theory close to the quantum critical point predicts a superconducting gap with spin-triplet symmetry for the ferromagnetic systems and a singlet gap for the nematic scenario. Studying fluctuations in this ordered phase using a nonlinear sigma model, we find that these fluctuations are not suppressed by a…
We analyze the finite-temperature phase diagram of the boson-fermion-Hubbard model with Feshbach converting interaction, using the coherent-state path-integral method. We show that depending on the position of the bosonic band, this type of interaction, even if weak, can drive the system into the resonant superfluid phase in the strong bosonic interaction limit. It turns out that this phase can exist for an arbitrary number of fermions (i.e., fermionic concentration between 0 and 2) but with the bosonic particle number very close to an integer value. We point out that the standard time-of-flig…
We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. Based on gauge invariance, we argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets t…
Fermionic superfluids can undergo phase transitions into different kinds of normal regimes, loosely characterized by whether Cooper pairs remain locally stable. If the normal phase retains strong pairing fluctuations, it behaves like a liquid of vortices, which has been observed in cuprate superconductors. We argue that analogous strongly correlated normal states exist in two-dimensional neutral fermion liquids near unitarity, where superfluid is destroyed by fast rotation. These states have non-universal properties, and if they develop as distinct thermodynamic phases they can be characterize…
The signature of superfluidity in bosonic systems is a sound wave-like spectrum of the single particle excitations which in the case of strong interactions is roughly temperature independent. In fermionic systems, where fermion pairing arises as a resonance phenomenon between free fermions and paired fermionic states (examples are: the atomic gases of lithium or potassium controlled by a Feshbach resonance, polaronic systems in the intermediary coupling regime, d-wave hole pairing in the strongly correlated Hubbard system), remnants of such superfluid characteristics are expected to be visible…
We determine the superfluid transition temperatures $T_c$ and the ground states of the attractive Hubbard model and find new insulating phases associated with non-integer filling at sufficiently strong pairing attraction $|U|$. These states, distinct from band and Mott insulating phases, derive from pair localization; pair hopping at large $|U|$ and high densities is impeded by inter-site, inter-pair repulsive interactions. The best way to detect the breakdown of superfluidity is using fermionic optical lattices which should reveal new forms of ``bosonic'' order, reflecting ground state pairin…
We study spinless electrons in a single channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity-coupled to an external superconductor, for an isolated wire there is no separate phase of a topological…
A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. Two canonically dual pairing gap functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due to the correlation holes. We find that the ground state is the Moore-Read pfaffian in the long wavelength limit for weak Coulomb interactions, a new pfaffian of an oscillatory pairing function for intermedi…
Doping a Mott-insulating $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*). Such a phase has several favorable features that make it a candidate for the pseudogap metal for the underdoped cuprates. We focus on a particular, simple $\mathbb{Z}_2$-FL* state which can undergo a confinement transition to a spatially uniform superconductor which is smoothly connected to the `plain vanilla' BCS superconductor with $d$-wave pairing. Such a transition occurs by the condensation of bosonic particles carrying $+e$ charge but no spin (`chargons'). We show that modifying the dispe…
In a recent preprint [0803.3052] A. Kanigel et al report evidence for Bogoliubov-type excitations in the pseudogap phase in the anti-nodal region, where a robust pseudogap remains well above Tc. This important experimental result has been theoretically predicted by us almost 6 years ago on a basis of the phenomenological boson fermion model. An earlier theoretical prediction on the basis of this model was that of a pseudogap in the electron DOS, setting in at some temperature T* and evolving into the superconducting gap upon approaching Tc. A natural logical pursuit of this early work was to s…
We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low density regime, the system phase-separates into a well defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of tightly bound bosonic pairs with a finite center-of-mass momentum tha…
