In material science, it was established that as the number of particles $ N $ in a material gets more and more, especially in the thermodynamic limit, various macroscopic quantum phenomena such as superconductivity, superfluidity, quantum magnetism, Fractional quantum Hall effects and various quantum or topological phase transitions (QPT) emerge in such non-relativistic quantum many-body systems. There is always a reservoir which exchanges energy and particles with the material. This is the essence of P. W. Anderson's great insight `` More is different ''. However, there is still a fundamental component missing in this general picture: How the `` More is different '' becomes different in a moving inertial frame or a moving sample? Here we address this outstanding problem.We demonstrate our claims by studying one of the simplest QPTs: Superfluid (SF)-Mott transitions of interacting bosons in a square lattice in a sample moving with a constant velocity $ \vec{v} $. We first elaborate the crucial difference between a moving sample and a moving inertial frame, stressing the crucial roles played by a reservoir in a grand canonical ensemble which is needed to study the SF-Mott transition in the first place. In this work, we mainly present the moving sample case and only discuss very briefly the moving inertial frame case. It is the moving which mixes the space and time. We also stress the important roles played by the underlying lattice. Doing various light or neutron scattering measurements in a moving sample may become an effective way not only measure various intrinsic properties of the materials, tune various quantum and topological phases through phase transitions, but also probe the new emergent space-time structure near any QPT.
In material science, it was established that as the number of particles N in a material gets more and more, especially in the thermodynamic limit, various macroscopic quantum phenomena such as superconductivity, superfluidity, quantum magnetism, Fractional quantum Hall effects and various quantum or topological phase transitions (QPT) emerge in such non-relativistic quantum many-body systems. There is always a reservoir which exchanges energy and particles with the material. This is the essence of P. W. Anderson's great insight More is different ''. However, there is still a fundamental component missing in this general picture: How the More is different '' becomes different in a moving inertial frame or a moving sample? Here we address this outstanding problem.We demonstrate our claims by studying one of the simplest QPTs: Superfluid (SF)-Mott transitions of interacting bosons in a square lattice in a sample moving with a constant velocity v. We first elaborate the crucial difference between a moving sample and a moving inertial frame, stressing the crucial roles played by a reservoir in a grand canonical ensemble which is needed to study the SF-Mott transition in the first place. In this work, we mainly present the moving sample case and only discuss very briefly the moving inertial frame case. It is the moving which mixes the space and time. We also stress the important roles played by the underlying lattice. Doing various light or neutron scattering measurements in a moving sample may become an effective way not only measure various intrinsic properties of the materials, tune various quantum and topological phases through phase transitions, but also probe the new emergent space-time structure near any QPT.
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.
The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum–space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high [Formula: see text] superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high [Formula: see text] cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.
The physics of strongly interacting particles is often extraordinarily rich, leading to the \textit{emergence} of fundamentally new phases and phenomena that cannot exist in the absence of correlations. This thesis is devoted to the study of different classes of quantum systems with such strong correlations. Programmable quantum simulators based on Rydberg atom arrays have recently emerged as versatile platforms to probe quantum many-body phases and their dynamics. In Chapter 2, we start with theories of quantum phase transitions (QPTs) in one-dimensional chains of Rydberg atoms. We demonstrate the existence of a novel QPT in the universality class of the Z3 chiral clock model, calculate its critical exponents, and discuss their measurement with the quantum Kibble-Zurek mechanism. Proceeding to two dimensions, Chapter 3 describes the zero-temperature phase diagram of a square-lattice Rydberg atom array, revealing several experimentally realizable density-wave-ordered phases and QPTs. For a different geometry, namely, the kagome lattice studied in Chapter 4, we identify a regime that constitutes a likely candidate for hosting a phase with long-range quantum entanglement and topological order. Based on mappings to dimer models and gauge theories, we argue for the existence of a quantum spin liquid phase that has proved elusive in solid-state materials. In the next part of this thesis, we focus on similarly strongly correlated phases in the realm of quantum materials. Motivated by recent observations of an enhanced thermal Hall response in the high-temperature cuprate superconductors, in Chapter 5, we study the thermal Hall conductivity, κxy, of chiral spin-liquid ans\"{a}tze on the square lattice, focusing on the contribution from neutral (bosonic or fermionic) spinons. Thereafter, going beyond mean-field theory, we consider the corrections due to emergent gauge fields, which yield a response of opposite sign to that of the fermionic matter. We additionally consider the contribution of phonons to κxy and establish its relation to the spinon Hall viscosity. Thermal Hall measurements also leave intriguing fingerprints in Kitaev materials like α-RuCl3, and in this context, Chapter 6 investigates the unquantized κxy obtained in a gapless spinon Fermi surface state.
One of the distinguishing achievements of physics has been the ability to describe the Universe based upon underlying microscopic principles. When there are many participating objects being governed by these microscopic principles, the resultant behavior often harbors emergent collective phenomena that may not be obviously related to the microscopic description. Phase transitions, quantum or classical, are a canonical example of such many-body phenomena that are understood in equilibrium through a framework of thermodynamic constraints, statistical ensembles, and a growth of system-wide correlations at the transition. However, a new class of quantum phase transitions has recently emerged for non-equilibrium systems with behavior that is not captured by this traditional framework. In the case of isolated quantum systems, these transitions occur among excited eigenstates and requires knowledge of the structure of these individual eigenstates in the quantum system. Understanding what drives such a phase transition requires a deeper microscopic knowledge of the role of correlations at the transition. \nThe use of ultracold atoms in optical lattices has paved the way for faithfully realizing quantum phase transitions. In particular, the advent of the quantum gas microscope realized an experimental platform that is highly controllable and provides microscopic access to the many-bodied wave functions. All experiments presented in this thesis use such a quantum gas microscope architecture where a quantum degenerate gas of Rb is used to probe the behavior of non-equilibrium quantum systems in one spatial dimension.\nThis thesis briefly discusses some studies of entanglement in equilibrium quantum phase transitions near the ground state of the system. In the first experiment, we directly measure the second-order R\\'enyi entanglement entropy that develops as a Bose-Hubbard system transitions from a Mott insulator to a superfluid. This is followed by a study of entanglement growth at the transition in the transverse Ising model. \nThese studies progress to the investigation of two particular non-equilibrium quantum phases and their transition into one another: quantum thermalization and many-body localization. We investigate the development of entanglement entropy that mimics thermodynamic entropy for an isolated quantum system which locally thermalizes under its own unitary dynamics. We then investigate the only known robust exception to this thermalizing behavior by studying the onset of many-body localization due to disorder. We observe the breakdown of thermalization in this phase and the logarithmically slow growth of entanglement throughout the system, which identifies the localized system to be an interacting one. Lastly, we investigate the role of correlations in the critical dynamics that emerge at high-orders where the system transitions from thermalizing behavior to many-body localization.
We study quantum phases and transitions in ultra-cold quantum gases, beyond the scope of conventional condensed matter systems. The study focuses on three major thrusts. The first thrust is the study of cold ensembles of bosonic or fermionic atoms in the higher orbital bands of optical lattices. Orbital and topological quantum physics is systematically explored for various lattice geometries, to be outlined below. The second is the low dimensional spin-imbalanced fermions in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We analyze its thermal instability towards Berezinsky-Kosterlitz-Thouless (BKT) phase transitions driven by different topological defects at finite temperature. The third is the theoretical search for a mechanism to achieve a Bose-Einstein crystal phase for bosons in the ground state. A new class of two-body interactions characterized by strong momentum-dependence is found to give rise to such a quantum state. It is different than but related to the long-debated concept of supersolidity. The first thrust forms the main part of the dissertation. Meta-stable phases of high orbital bosons and fermions have been explored for different lattice geometries such as square and bipartite lattices. Exotic Mott and superfluid phases are studied in both one and two dimensions. Quantum and thermal phase transitions, associated with time reversal symmetry breaking and their experimental signatures are discussed. In particular a quantum ``disordered" superfluid phase, beyond the mean field description, is found in one dimension. The challenging problem of probing time reversal symmetry breaking is solved. Besides, a one-dimensional fermionic optical ladder with coupled s- and p-orbitals is shown to mimic spin-orbit interactions and exhibit topological insulator and topological superconducting phases. Charge fractionalization is shown to be realizable in such an sp-orbital ladder.
The main objective of this paper is to provide a systematic theoretical study on quantum phase transitions associated with the Bose-Einstein condensates, the superfluidity and the su-perconductivity. First, we indicate that there are only two types of phase transitions: dynamical phase transitions and topologi-cal phase transitions (TPTs). A TPT refers to the transition in its topological structure in the physical space of the system, and quantum phase transitions (QPTs) belong to the category of TPTs. Second, the basic physical characteristics of a QPT are precisely formulated. In particular, a QPT is a transition between quantum states, which are described by the wave functions ψ, and the control parameters are non-thermal. Third, we derive the topological structure equations for QPTs, so that the basic geometric theory of incompressible flows can be readily applied. In particular, a topo-logical index for the supercurrent can be defined, leading to precise information on the topological structure and its transitions in the physical space for the underlying system. Fourth, we derive then the basic theory for different TPTs, leading to transparent physical pictures of various condensates. Finally, we derive the microscopic mechanism for the Meissner effect of superconductivity: below the critical temperature, under the applied magnetic field, spin J = 1 Cooper pairs reversely parallel to the applied field can form and are stable, and the total magnetic moment of all Cooper pairs, together with the surface supercurrent, can cancel out the magnetism induced by the applied field and resists the applied field from entering its body.