We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

https://arxiv.org/pdf/cond-mat/0102119.pdf

Quantum Phase Transitions

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials Quantum simulation of condensed-matter systems using ultracold atoms provides a way to study problems that are computationally intractable on classical computers Using an ultracold gas of rubidium atoms confined in an optical lattice, Simon et al simulate quantum magnetism in a chain of spins and observe a quantum phase transition from a paramagnetic phase into an antiferromagnetic phase This work provides a tunable platform for studies of magnetic quantum phase transitions, which have been realized in few real materials

/pdf/quantum-simulation-of-antiferromagnetic-spin-chains-in-an-17pm6p6aiv.pdf

Quantum simulation of antiferromagnetic spin chains in an optical lattice

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

http://science.sciencemag.org/content/sci/327/5962/177.full.pdf

Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications from high temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers due to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we employ a degenerate Bose gas confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary an applied field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase the interaction between the spins is overwhelmed by the applied field which aligns the spins. In the antiferromagnetic phase the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in-situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, improving our understanding of real magnetic materials.

Quantum Simulation of an Antiferromagnetic Spin Chain in an Optical Lattice

The Bose–Einstein condensate (BEC) is a fascinating state of matter predicted to occur for particles obeying Bose statistics. Although the BEC has been observed with bosonic atoms in liquid helium and cold gases, the concept is much more general. We here review analogous states, where excitations in magnetic insulators form the BEC. In antiferromagnets, elementary excitations are magnons, quasiparticles with integer spin and Bose statistics. In certain experiments their density can be controlled by an applied magnetic field leading to the formation of a BEC. Furthermore, interactions between the excitations and the interplay with the crystalline lattice produce very rich physics compared with the canonical BEC. Studies of magnon condensation in a growing number of magnetic materials thus provide a unique window into an exciting world of quantum phase transitions and exotic quantum states, with striking parallels to phenomena studied in ultracold atomic gases in optical lattices. A collection of bosonic particles, such as liquid helium or ultracold gases, can condense into a ground state in which the atoms flow as a ‘superfluid’ without scattering. Magnetic materials further illustrate the generality of the effect, as described in this review.

Bose–Einstein condensation in magnetic insulators

We follow the evolution of the elementary excitations of the quantum antiferromagnet TlCuCl3 through the pressure-induced quantum critical point, which separates a dimer-based quantum disordered phase from a phase of long-ranged magnetic order. We demonstrate by neutron spectroscopy the continuous emergence in the weakly ordered state of a low-lying but massive excitation corresponding to longitudinal fluctuations of the magnetic moment. This mode is not present in a classical description of ordered magnets, but is a direct consequence of the quantum critical point.

/pdf/quantum-magnets-under-pressure-controlling-elementary-rxv3cott1w.pdf

Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3

The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.

/pdf/multiple-magnon-modes-and-consequences-for-the-bose-einstein-3x96dp5w95.pdf

Multiple magnon modes and consequences for the Bose-Einstein condensed phase in BaCuSi2O6.

EIGER is the new thermal triple-axis-spectrometer at the continuous spallation SINQ at PSI. The shielding of the monochromator consists only of non- or low magnetizable materials, which allows the use of strong magnetic fields with the instrument. This shielding reduces the high energy neutron contamination to a comparable level of thermal spectrometers at reactor sources. The instrument design, the performance and first results of the spectrometer are presented.

S. N. Gvasaliya

Papers

Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3

Multiple magnon modes and consequences for the Bose-Einstein condensed phase in BaCuSi2O6.

The thermal triple-axis-spectrometer EIGER at the continuous spallation source SINQ