This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the past twenty years, we should no longer be surprised that superconductivity emerges as a highly competitive ground state in systems where Coulomb repulsion plays a dominant role. The physics of the cuprates is discussed, emphasizing the unusual pseudogap phase in the underdoped region. It is argued that the resonating valence bond picture, as formulated using gauge theory with fermionic and bosonic matter fields, gives an adequate physical understanding, even though many details are beyond the powers of current calculational tools. The recent discovery of quantum oscillations in a high magnetic field is discussed in this context. Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high T c problem where significant progress has been made recently. It is understood that the existence of matter fields can lead to deconfinement of the U (1) gauge theory in 2 + 1 dimensions, and novel new particles (called fractionalized particles), such as fermionic spinons which carry spin and no charge, and gapless gauge bosons can emerge to create a new critical state at low energies. We even have a couple of real materials where such a scenario may be realized experimentally. The paper ends with answers to questions such as: What limits T c if pairing is driven by an electronic energy scale? Why is the high T c problem hard? Why is there no consensus? And why is the high T c problem important?
This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the past twenty years, we should no longer be surprised that superconductivity emerges as a highly competitive ground state in systems where Coulomb repulsion plays a dominant role. The physics of the cuprates is discussed, emphasizing the unusual pseudogap phase in the underdoped region. It is argued that the resonating valence bond picture, as formulated using gauge theory with fermionic and bosonic matter fields, gives an adequate physical understanding, even though many details are beyond the powers of current calculational tools. The recent discovery of quantum oscillations in a high magnetic field is discussed in this context. Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high T c problem where significant progress has been made recently. It is understood that the existence of matter fields can lead to deconfinement of the U (1) gauge theory in 2 + 1 dimensions, and novel new particles (called fractionalized particles), such as fermionic spinons which carry spin and no charge, and gapless gauge bosons can emerge to create a new critical state at low energies. We even have a couple of real materials where such a scenario may be realized experimentally. The paper ends with answers to questions such as: What limits T c if pairing is driven by an electronic energy scale? Why is the high T c problem hard? Why is there no consensus? And why is the high T c problem important?
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.
Bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-Tc cuprates and other systems
The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-Tc cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-Tc cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature Tc and then such bosons condenses into a Bose superfluid at Tc. The pair condensation of attracting bosons occurs at Tc and then their single particle condensation sets in at Tc∗ lower than Tc (in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below Tc. By solving the mean field equations for high-Tc cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature Tv=Tc2D lower than T* but higher than Tc=Tc3D and two superconducting phases below Tc) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
Strongly correlated electron systems (SCES) represent a class of quantum materials where electron-electron interactions play a dominant role in determining physical properties, leading to a wide array of exotic phenomena such as high-temperature superconductivity, quantum spin liquids, Mott transitions, and heavy fermion behavior. Unlike weakly interacting systems described adequately by Fermi-liquid theory, SCES require more advanced theoretical frameworks due to the breakdown of single-particle descriptions. This article reviews the fundamental interactions governing SCES, emphasizing Coulomb repulsion, spin-charge separation, and entanglement-driven effects. The role of lattice geometry, orbital degeneracy, and dimensionality is explored to understand emergent behaviors. Through theoretical insights and recent experimental findings, this work outlines how these fundamental interactions shape the rich phase diagrams of SCES and their implications in quantum technologies.
Experiments on strongly correlated quasi-two-dimensional electronic materials---for example, the high-temperature cuprate superconductors and the putative quantum spin liquids kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2---routinely reveal highly mysterious quantum behavior which cannot be explained in terms of weakly interacting degrees of freedom. Theoretical progress thus requires the introduction of completely new concepts and machinery beyond the traditional framework of the band theory of solids and its interacting counterpart, Landau's Fermi liquid theory. In full two dimensions, controlled and reliable analytical approaches to such problems are severely lacking, as are numerical simulations of even the simplest of model Hamiltonians due to the infamous fermionic sign problem.Here, we attempt to circumvent some of these difficulties by studying analogous problems in quasi-one dimension. In this lower dimensional setting, theoretical and numerical tractability are on much stronger footing due to the methods of bosonization and the density matrix renormalization group, respectively. Using these techniques, we attack two problems: (1) the Mott transition between a Fermi liquid metal and a quantum spin liquid as potentially directly relevant to the organic compounds kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2 and (2) non-Fermi liquid metals as strongly motivated by the strange metal phase observed in the cuprates. In both cases, we are able to realize highly exotic quantum phases as ground states of reasonable microscopic models. This lends strong credence to respective underlying slave-particle descriptions of the low-energy physics, which are inherently strongly interacting and also unconventional in comparison to weakly interacting alternatives.Finally, working in two dimensions directly, we propose a new slave-particle theory which explains in a universal way many of the intriguing experimental results of the triangular lattice organic spin liquid candidates kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. With use of large-scale variational Monte Carlo calculations, we show that this new state has very competitive trial energy in an effective spin model thought to describe the essential features of the real materials.
Ever since the introduction of resonating valence bond states by P.\\ W.\\ Anderson in 1970s, the search for exotic many--body quantum behavior in peculiar states of matter known as quantum spin liquids has been a central challenge in the field of condensed matter physics. An important searching ground for such \\emph{quantum--ness} is the low energy physics of frustrated magnets. In a quantum system, frustration---the inability of a physical system to achieve a global state that consistently minimizes its energy locally---enables the unavoidable quantum fluctuations to hybridize an extensive number of classical states into highly entangled quantum states at low temperatures. It can be argued that this is the most practical approach to achieve genuine many--body quantum behavior at large scales. The fundamental source of frustration in many physical systems, is the existence of local non--commuting terms. In the case of antiferromagnet spin theories the simplest examples are triangles of nearest--neighboring sites. Consequently, lattices with triangles as building blocks have long been studied in hopes of discovering spin liquids physics. In particular the kagome lattice, which is composed of corner--sharing triangles, has been the center of at least four decades of spin liquid research. This is due to the underconstrained nature of system made out of corner--sharing triangles. After the first three chapters, introduction in chapter~\\ref{chap:intro}, preliminary physics in chapter~\\ref{chap:prelim}, and a brief introduction to spin--liquids in chapter~\\ref{chap:QSLs}, in chapter~\\ref{chap:kagome} I tackle a simpler version of the long-standing problem of spin--1/2 Heisenberg antiferromagnets by considering a quasi--1D lattice consisting entirely of corner--sharing triangles, \\emph{kagome strip}. I illustrate that the standard Heisenberg antiferromagnet Hamiltonian over kagome strip is an extended gapless quantum phase, that is well characterized by two fermionic/bosonic gapless modes and power--law decaying spin and bond--energy correlations. I also demonstrate that the correlation functions oscillate at tunably incommensurate wave vectors. It turns out that this phase can be identified by a particular marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field. This interpretation is supported by analytic Abelian bosonization and with extensive numerical large--scale density matrix renormalization group study as well as variational Monte Carlo calculations on Gutzwiller ans\\"atz wave functions. This intriguing result is the first numerical demonstration of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly 1D (Bethe chain) limit. The unexpected success of the fermionic spinons in describing the low energy physics of kagome antiferromagnet, reintroduces the questions about the validity of spinon physics as an effective theory of quantum spin liquids. However, numerical methods are still far behind the theoretical advances. And still even today, an accurate description of the quantum spin liquid states using tensor network methods is notoriously challenging. It is known that for large quasi-1D systems, the density matrix renormalization group and related methods usually require significant computational resources and sometimes fail to converge to a satisfactory state. On the other hand, variational wavefunctions acquired from the Gutzwiller projection of gaussian fermionic theories have long served as both a theoretical starting point for the construction of such spin liquid states and as an inspiration for numerical variational Monte Carlo (VMC) to calculate observables of interest. Noting this observation I examine a different method by exploring the possibility of constructing a matrix product state (MPS) representation for a Gutzwiller--projected state from two given MPS representations of gaussian fermionic theories in the \\ref{chap:gutz} chapter. I investigate the complexity of different approaches to achieve Gutzwiller projection for MPSs and introduce the novel algorithm which we call the Guzwiller zipper method. The performance of the algorithm is tested against two copies of a single half-filled band of spin-1/2 fermionic spinons. In a successful attempt to describe the nature of spin liquid states on quasi-1D strips of triangular and kagome-like lattices, I apply this method to two MPS of multi-band fermionic spinon theories and compare with the complexity of the traditional VMC approach. In particular, we methodically disprove the conjecture of a spinon fermi surface spin liquid for the triangular lattice. Finally, I conclude this thesis by laying out a bird's eye view of the current and future of spin liquid physics in kagome and triangular lattices and pointing out numerous possible applications of the novel Gutzwiller zipper method. In addition, I would also discuss its possible extensions to more complicated tensor networks as well as versions for higher spatial dimensions.