Spectral divergences have long been important in physics, from the 19th century UV catastrophe to IR divergences in modern quantum field theory. In all these, ``feedback'' mechanisms quell the divergences. But what if multiple IR divergences -- soft photons, phonons, and electronuclear magnons -- conspire to produce finite decoherence at a quantum phase transition? The authors develop here the theory for these cancelling divergences and experimentally observe the resulting mode softening in a quantum Ising magnet, with implications from condensed matter to quantum gravity.
Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.
Quantum phase transitions in spin systems are supposed to be accompanied by a soft collective mode, which has not been seen in experiments. Here, we directly measure the low energy excitation modes of a well-known realization of the Ising model in transverse field, LiHoF
4, using microwave spectroscopy techniques to probe energies well below what is accessible via neutron scattering experiments. Instead of the single excitation expected for a simple quantum Ising system, we find and characterize a remarkable array of `electronuclear' modes, arising from coupling of the spin-1/2 Ising electronic spins to a bath of spin-7/2 Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point from below and above, a softening that can be quenched with the application of a longitudinal magnetic field. The electronuclear mode structure has direct implications for the Ising systems that serve as the building blocks of adiabatic quantum computers and quantum annealers.
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.
We consider a linear quench from the paramagnetic to ferromagnetic phase in the quantum Ising chain interacting with a static spin environment. Both decoherence from the environment and nonadiabaticity of the evolution near a critical point excite the system from the final ferromagnetic ground state. For weak decoherence and relatively fast quenches the excitation energy, proportional to the number of kinks in the final state, decays like an inverse square root of a quench time, but slow transitions or strong decoherence makes it decay in a much slower logarithmic way. We also find that fidelity between the final ferromagnetic ground state and a final state after a quench decays exponentially with a size of a chain, with a decay rate proportional to average density of excited kinks and a proportionality factor evolving from 1.3 for weak decoherence and fast quenches to approximately 1 for slow transitions or strong decoherence. Simultaneously, correlations between kinks randomly distributed along the chain evolve from a near-crystalline antibunching to a Poissonian distribution of kinks in a number of isolated Anderson localization centers randomly scattered along the chain.
We discuss spin-
21 one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor
J1 and antiferromagnetic next-nearest-neighbor
J exchange interactions in a strong magnetic field
H. It is well known that, due to attraction between magnons, quantum phase transitions (QPTs) take place at
H=Hs from the fully polarized phase to the nematic phase if
J>∣J1∣/4. Such a transition at
J>0.368∣J1∣ is characterized by a softening of the two-magnon bound-state spectrum. Using a bond-operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations whose spectrum coincides at $H\ensuremath{\ge}{H}_{s}$ with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at
H=Hs makes the QPT consideration substantially standard. In the 1D case at
H<Hs, we find an expression for the magnetization which well describes existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before, either in the limiting case of $J\ensuremath{\gg}|{J}_{1}|$ or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the
H-
T plane between the fully polarized and the nematic phases is given by ${H}_{s}(0)\ensuremath{-}{H}_{s}(T)\ensuremath{\propto}{T}^{3/2}$. Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization, and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to
1/ln(1+∣J1∣/J). Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel.
To this day, von Neumann definition of entropy remains the most popular measure of quantum entanglement. Much of the literature on entanglement entropy, particularly in the context of field theory, has focused on isolating the UV divergences. IR divergences of the entanglement entropy are less studied in this context, and apart from being easier to isolate, they offer an interesting insight into the physics of the system, such as the role of zero modes in these divergences. To gain a better understanding of the system in this limit, we develop the free particle approximation of Harmonic oscillator, with which we investigate the properties of entropy divergence in continuous bi-partite quantum systems such as the coupled Harmonic oscillators and the Hydrogen atom. We also show IR divergence of the entropy of environment-induced entanglement in a tri-partite oscillator system. We discuss the implications of our result for field theory and IR structure of gravity.