This study has a look at investigates quantum phase transitions (QPTs) in low-dimensional substances, focusing at the outcomes of disorder, electron interactions, and outside fields. Theoretical frameworks, which includes the Hubbard and Ising models, have been employed to analyze essential behaviors, at the same time as renormalization organization strategies furnished insights into scaling near quantum critical points. Experimental observations of conductivity below varying magnetic fields and ultra-low temperatures showed segment transitions between steel, insulating, and superconducting states. These findings were in addition verified via computational simulations using Density Functional Theory (DFT) and Quantum Monte Carlo (QMC) methods, which correctly mapped phase diagrams and important temperatures. The effects underscore the transformative potential of QPTs in quantum technologies, in particular in the development of solid qubits and green nanoelectronics gadgets. Future research will awareness on refining theoretical fashions, enhancing experimental setups, and exploring new quantum levels to increase quantum and nano technology.
This study has a look at investigates quantum phase transitions (QPTs) in low-dimensional substances, focusing at the outcomes of disorder, electron interactions, and outside fields. Theoretical frameworks, which includes the Hubbard and Ising models, have been employed to analyze essential behaviors, at the same time as renormalization organization strategies furnished insights into scaling near quantum critical points. Experimental observations of conductivity below varying magnetic fields and ultra-low temperatures showed segment transitions between steel, insulating, and superconducting states. These findings were in addition verified via computational simulations using Density Functional Theory (DFT) and Quantum Monte Carlo (QMC) methods, which correctly mapped phase diagrams and important temperatures. The effects underscore the transformative potential of QPTs in quantum technologies, in particular in the development of solid qubits and green nanoelectronics gadgets. Future research will awareness on refining theoretical fashions, enhancing experimental setups, and exploring new quantum levels to increase quantum and nano technology.
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions, driven by experiments on cuprate superconductors, heavy fermion materials, organic conductors, and related compounds. Although quantum phase transitions in simple spin systems, like the Ising model in a transverse field, were studied in the early 1970s, much of the subsequent theoretical work examined a particular example: the metal–insulator transition. While this is a subject of considerable experimental importance, the greatest theoretical progress was made for the case of the Anderson transition of non-interacting electrons, which is driven by localization of the electronic states in the presence of a random potential. The critical properties of this transition of noninteracting electrons constituted the primary basis upon which most condensed matter physicists have formed their intuition on the behavior of the systems near a quantum phase transition. However, it is clear that strong electronic interactions play a crucial role in the systems of current interest noted earlier, and simple paradigms for the behavior of such systems near quantum critical points are not widely known. It is the purpose of this book to move interactions to center stage by describing and classifying the physical properties of the simplest interacting systems undergoing a quantum phase transition. The effects of disorder will be neglected for the most part but will be considered in the concluding chapters. Our focus will be on the dynamical properties of such systems at nonzero temperature, and it will become apparent that these differ substantially from the noninteracting case.
The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms for these QPTs have been proposed, it remains unclear which, if any, are applicable to a specific two-dimensional superconducting system. Here, we find that a pair-breaking mechanism which suppresses the Cooper pair density gives a unifying description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, and the high-temperature superconductor La1.92Sr0.08CuO4. This transition occurs within the superconducting subsystem and is masked by the dominant non-critical contribution of normal electrons. The discovery was enabled by the development of a QPT model that goes beyond the conventional determination of the critical exponents and incorporates into the analysis a microscopic length scale characterizing the transitions. We found that in the materials studied, and MoGe nanowires, this scale corresponds to the size of a Cooper pair. The model has also been successfully applied to QPTs in Josephson junction arrays and various non-superconducting materials. The observation that microscopic scales are encoded in the scaled experimental data of QPTs likely extends beyond equilibrium condensed matter physics and may reveal underlying principles of critical phenomena in a wide variety of systems.
Strongly correlated low-dimensional quantum spin models provide a well-established frame- \nwork to study magnetic properties of insulators, and are of great theoretical interest and experimental relevance in condensed-matter physics. In this thesis, I use quantum Monte Carlo methods to numerically study quantum critical behavior in low-dimensional quantum spin models and wavefunctions. \n \nFirst, I study spinons &ndash emergent spin-1/2 bosonic excitations &ndash at certain one- and two-dimensional quantum phase transitions (QPTs) in spin models, by characterizing their size and confinement length quantitatively. In particular, I focus on the QPT from an antiferromagnetic (AFM) phase into a valence-bond solid (VBS) phase, which is an example of a violation of the standard Landau-Ginzburg-Wilson paradigm for phase transitions. This transition in two dimensions (2D) is instead likely described by a novel theory called "deconfined quantum criticality" (DQC). According to the theory, spinons should be deconfined. The degree of deconfinement is quantified in my calculations. \n \nSecond, I present a comprehensive study of so-called short-bond resonating-valence-bond (RVB) spin liquids in 2D, which have been suggested as a good starting point for understanding the spin physics of high-temperature cuprates. I find that these RVB states can also be classified as quantum-critical VBS states, which indicates that RVB is less disordered than expected. This work suggests a possible mapping from the quantum RVB states to classical dimer models via a classical continuum field theory--the height model. This map explicitly bridges well-established classical results to future quantum studies. \n \nThird, I consider 1D amplitude product (AP) states, which are generalized versions of RVB states, with different wavefunction weightings of bonds according to their lengths. AP states constitute a good ansatz for certain Hamiltonians and are of broad interest in quantum magnetism. I study phase transitions from AFM-VBS phases in AP states by tuning their amplitudes, and obtain continuously varying critical exponents. In addition, I classify the 1D AP states through entanglement entropy calculations of the central charge in (1+1)D conformal field theory. This new classification could serve as guide for AP states as trial wavefunctions to search for ground states of corresponding quantum spin models.
Quantum phase transition arises in general as second order phase transition at zero temperature, tuned by a non-thermal parameter such as pressure, doping or a magnetic field. The point in the phase diagram of the material in which different phases meet is called a quantum critical point (QCP). Physics around QCPs are of extensive current interest because the critical quantum fluctuations influence the physical properties in a wide temperature range (quantum criticality), and are believed to be responsible for many emergent physical properties such as non-Fermi liquids and unconventional superconductivity. In this research we explore dynamics and thermodynamics near QCPs via investigating three classes of models, which all have real material correspondence. Specifically first, we study local dynamics in a perturbed quantum critical Ising chain with E8 symmetry, where we show the local dynamical spin susceptibility has a singular dependence on frequency, but differs from the diffusion form. The nuclear magnetic resonance (NMR) relaxation rate at low temperatures depends exponentially on the inverse temperature, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E8 description for CoNb2O6. Second, we investigate the thermodynamic properties of itinerant ferromagnets near quantum critical points, described by the quantum Landau-Ginzburg theory. We provide a regularized perturbative renormalization group procedure to calculate the free energy. We further carry out numerical calculations on thermodynamic quantities, capturing not only the leading critical behaviors, but also the subleading and nonsingular contributions. We demonstrate various thermodynamic signatures of quantum criticality, including the entropy accumulation effect and the divergence of the specific heat coefficient. A detailed comparison to the recent experimental results on an itinerant ferromagnet Sr3Ru2O7 is also presented. Third, we explore Ising-nematic and magnetic phases and their transitions in iso-electronically doped iron pnictides by carrying out a large-N study of an effective low-energy Ginzburg-Landau model for these systems. We demonstrate that the magnetic and Ising orders transitions are concurrent at zero temperature, and both transitions are weakly first-order, which is consistent with RG-based prediction and experimental observations.
Over the past four decades, experimental studies of quantum phase transitions (QPTs) have been primarily focused on identifying these transitions in various materials and determining the critical exponents and universality classes associated with them. Since the critical exponents originate from the scale invariance, they are not explicitly tied to the microscopic physics of QPTs, which remains poorly understood for many systems. We have developed a model of QPTs, which addresses this deficiency. The model is based on the experimentally supported conjecture that the scaled data across a QPT depend, in a universal manner, on two system-specific length scales: the microscopic scale, L0, typically known from general considerations (e.g., mean-free path, lattice constant) and the dephasing length, ${L}_{\ensuremath{\varphi}}(T)$. Using this model, we have found that experimental data in the quantum critical regime of 18 distinct material classes can be quantitatively described by assuming that ${L}_{\ensuremath{\varphi}}(T)$ is determined by the distance traveled by system-specific excitations during the Planckian time, ${\ensuremath{\tau}}_{P}=\ensuremath{\hbar}/{k}_{B}T$. In this work, we demonstrate how the model explains microscopic physics of QPTs in doped semiconductors and amorphous alloys, materials with Ising and Heisenberg spin chains, cold boson gases in optical traps, and the Mott transitions in organic semiconductors. The dynamics of excitations is determined by parameters such as the effective mass and diffusion coefficient, D, of the corresponding noninteracting or weakly renormalized system. For doped semiconductors and amorphous alloys, the noncritical behavior of D in the quantum critical regime sharply contrasts with zero-temperature diffusion coefficient, which goes to zero at the transition. We also analyze the results of numerical studies of the Mott transition with dynamical mean-field theory, interpreting them as if they were experimental data. For these results, we find that, as expected, the microscopic scale matches the dimensionless lattice constant, ${L}_{0}\ensuremath{\sim}1$. Finally, we report that the metal-insulator transition in Si:P, Ge:Sb, and Ge:As can be explained using a noninteracting version of the model.
Classical and quantum spin systems are widely used models in both experimental and theoretical condensed matter physics. In many materials, the electronic interactions can be difficult to model exactly. However, in some insulators (Mott insulators), the magnetic (spin) interactions can be captured well with spin-only models. Several models are studied in this thesis. First, I report the solution of a long-standing issue in a classical frustrated spin model (i.e., where the quantum effects are neglected and the complexity is due to competing interactions): the nature of the thermal phase transition to a stripe state in the two dimensional (2D) J1-J2 model. Here J1 and J2 are nearest- and next-nearest-neighbor couplings. Monte Carlo simulations with single-spin updates are used for the calculations, and an extended-ensemble method, a generalization of the Wang-Landau algorithm, is also developed and tested. I focus on the study of "weak universality" behavior (continuously varying critical exponents, with one of the exponents staying fixed), for which I show a correspondence with a known class of conformal field theories with charge c = 1. Next, moving to quantum spins, to shed light on magnetic systems studied experimentally and to investigate new types of quantum states of interest in developing theories of quantum magnetism, I study the S = 1/2 Heisenberg model on the 2D square lattice with added six-spin interactions (the so-called J-Q3 model) as well as a set of 3D quantum antiferromagnets on dimerized lattices. Here I use the stochastic series expansion quantum Monte Carlo method. In the study of the J-Q3 model, I report on a similar weak-universality behavior as in the classical J1-J2 model, but with a mapping to a different known class of c = 1 conformal field theories. The critical behavior of the system again shows continuously changing exponents, in a way which corresponds to a gradual weakening of Z4 symmetry-breaking to an emergent U(1) symmetry. In the study of dimerized antiferromagnets, I report on a universal behavior of the Néel temperature TN, which can be related to ground state parameters independently of the microscopic interaction details in several different models.