Order Quantum Phase Transition Research Articles

Superconducting scanning tunneling microscopy tips in a magnetic field: Geometry-controlled order of the phase transition

The properties of geometrically confined superconductors significantly differ from their bulk counterparts. Here, we demonstrate the geometrical impact for superconducting scanning tunneling microscopy (STM) tips, where the confinement ranges from the atomic to the mesoscopic scale. To this end, we compare the experimentally determined magnetic field dependence for several vanadium tips to microscopic calculations based on the Usadel equation. For our theoretical model of a superconducting cone, we find a direct correlation between the geometry and the order of the superconducting phase transition. Increasing the opening angle of the cone changes the phase transition from first to second order. Comparing our experimental findings to the theory reveals first and second order quantum phase transitions in the vanadium STM tips. In addition, the theory also explains experimentally observed broadening effects by the specific tip geometry.

Holographic phase transitions from higgsed, non abelian charged black holes

We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the case of $p+ip$-wave superconductors the transitions are always of second order. But for $p$-wave superconductors we determine the existence of a critical value $\alpha_c$ of the gravitational coupling (for fixed Higgs v.e.v. parameter $\hat m_W$) beyond which the transitions become of first order. As a by-product, we show that the $p$-wave phase is energetically favored over the $p+ip$ one, for any values of the parameters. We also find the ground state solutions corresponding to zero temperature. Such states are described by domain wall geometries that interpolate between $AdS_4$ spaces with different light velocities, and for a given $\hat m_{W}$, they exist below a critical value of the coupling. The behavior of the order parameter as function of the gravitational coupling near the critical coupling suggests the presence of second order quantum phase transitions. We finally study the dependence of the solution on the Higgs coupling, and find the existence of a critical value beyond which no condensed solution is present.

Hovering black holes from charged defects

We construct the holographic dual of an electrically charged, localized defect in a conformal field theory at strong coupling, by applying a spatially dependent chemical potential. We find that the infrared behaviour of the spacetime depends on the spatial falloff of the potential. Moreover, for sufficiently localized defects with large amplitude, we find that a new gravitational phenomenon occurs: a spherical extremal charged black hole nucleates in the bulk: a hovering black hole. This is a second order quantum phase transition. We construct this new phase with several profiles for the chemical potential and study its properties. We find an apparently universal behaviour for the entropy of the defect as a function of its amplitude. We comment on the possible field theory implications of our results.

Universal order parameters and quantum phase transitions: a finite-size approach.

We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm.

Geometric critical exponents in classical and quantum phase transitions.

We define geometric critical exponents for systems that undergo continuous second-order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two-dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.

Quantum critical dynamics of the boson system in the Ginzburg–Landau model

The quantum critical dynamics of the quantum phase transitions is considered. In the framework of the unified theory, based on the Keldysh technique, we consider the crossover from the classical to the quantum description of the boson many-body system dynamics close to the second order quantum phase transition. It is shown that in this case the upper critical space dimension of this model is dc+=2, therefore the quantum critical dynamics approach is useful in case of d<2. In the one-dimension system the phase coherence time does diverge at the quantum critical point, gc, and has the form of τ∝−ln∣g−gc∣/∣g−gc∣, the correlation radius diverges as rc∝∣g−gc∣−ν(ν=0.6).

A quantum critical point from flavours on a compact space

We analyse a $2+1$ dimensional defect field theory on a two sphere in an external magnetic field. The theory is holographically dual to probe D5-branes in global AdS$_5\times S^5$ background. At any finite magnetic field only the confined phase of the theory is realised. There is a first order quantum phase transition, within the confined phase of theory, ending on a quantum critical point of a second order phase transition. We analyse the condensate and magnetisation of theory and construct its phase diagram. We study the critical exponents near the quantum critical point and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of $-2/3$. Next, we analyse the meson spectrum of the theory and identify a massless mode at the critical point signalling a diverging correlation length of the quantum fluctuations. We find that the derivative of the meson mass with respect to the bare mass also diverges with a critical exponent of $-2/3$. Finally, our studies of the magnetisation uncover a persistent diamagnetic response similar to that in mesoscopic systems, such as quantum dots and nano tubes.

Many-body formation and dissociation of a dipolar chain crystal

We propose an experimental scheme to effectively assemble chains of dipolar gases with a uniform length in a multi-layer system. The obtained dipolar chains can form a chain crystal with the system temperature easily controlled by the initial lattice potential and the external field strength during processing. When the density of chains increases, we further observe a second order quantum phase transition for the chain crystal to be dissociated toward layers of 2D crystal, where the quantum fluctuation dominates the classical energy and the compressibility diverges at the phase boundary. The experimental implication of such a dipolar chain crystal and its quantum phase transition is also discussed.

Work and quantum phase transitions: quantum latency.

We study the physics of quantum phase transitions from the perspective of nonequilibrium thermodynamics. For first-order quantum phase transitions, we find that the average work done per quench in crossing the critical point is discontinuous. This leads us to introduce the quantum latent work in analogy with the classical latent heat of first order classical phase transitions. For second order quantum phase transitions the irreversible work is closely related to the fidelity susceptibility for weak sudden quenches of the system Hamiltonian. We demonstrate our ideas with numerical simulations of first, second, and infinite order phase transitions in various spin chain models.

First- and Second-Order Phase Transition in Parallel Triple Quantum Dots: The Roles of Symmetric and Asymmetric Hopping

By means of the numerical renormalization group method, I study the quantum phase transition (QPT) and the electronic transport in parallel triple quantum dot system with symmetric and/or asymmetric hopping. For symmetric hopping $$t_{1} = t_{2}$$ and zero magnetic field $$B = 0$$ , I find a first order transition between spin quadruplet and doublet as $$t_{1}$$ ( $$t_{2}$$ ) increases. With increasing $$B$$ , a second order QPT between $$S_{z} = 1/2$$ of the doublet and $$S_{z} = 3/2$$ of the quadruplet is observed. For asymmetric hopping $$t_{1} \ne t_{2}$$ , the QPT depends closely on the other hopping. For fixed $$t_{1} < \varGamma $$ , where $$\varGamma $$ is the hybridization function between the dots and the leads, a first order transition is observed as $$t_{2}$$ increases, while for $$t_{1} \ge \varGamma $$ , a crossover occurs. In the presence of $$B$$ , the transition between $$S_{z} = 1/2$$ and $$S_{z} = 3/2$$ is a first order QPT for $$t_{1} < \varGamma $$ , while a second order for $$t_{1} \ge \varGamma $$ .

Imprints of spin-orbit density wave in the hidden-order state of URu2Si2

The mysterious second order quantum phase transition, commonly attributed to the `hidden-order' (HO) state, in heavy-fermion metal URu2Si2 exhibits a number of paradoxical electronic and magnetic properties which cannot be associated with any conventional order parameter. We characterize and reconcile these exotic properties of the HO state based on a spin-orbit density wave order (SODW), constructed on the basis of a realistic density-functional theory (DFT) band structure. We quantify the nature of the gapped electronic and magnetic excitation spectrum, in agreement with measurements, while the magnetic moment is calculated to be zero owing to the spin-orbit coupling induced time-reversal invariance. Furthermore, a new collective mode in the spin-1 excitation spectrum is predicted to localize at zero momentum transfer in the HO state which can be visualized, for example, by electron spin resonance (ESR) at zero magnetic field or polarized inelastic neutron scattering measurements. The results demonstrate that the concomitant broken and invariant symmetries protected SODW order not only provides insights into numerous nontrivial hidden-order phenomena, but also offers a parallel laboratory to the formation of a topologically protected quantum state beyond the quantum spin-Hall state and Weyl semimetals.

Bound states at impurities as a probe of topological superconductivity in nanowires

Spin-orbit coupled superconductors are potentially interesting candidates for realizing topological and potentially non-Abelian states with Majorana Fermions. We argue that time-reversal broken spin-orbit coupled superconductors generically can be characterized as having sub-gap states that are bound to localized non-magnetic impurities. Such bound states, which are referred to as Shiba states, can be detected as sharp resonances in the tunneling spectrum of the spin-orbit coupled superconductors. The Shiba state resonance can be tuned using a gate-voltage or a magnetic field from being at the edge of the gap at zero magnetic fields to crossing zero energy when the Zeeman splitting is tuned into the topological superconducting regime. The zero-crossing signifies a Fermion parity changing first order quantum phase transition, which is characterized by a Pfaffian topological invariant. These zero-crossings of the impurity level can be used to locally characterize the topological superconducting state from tunneling experiments.

Flavoured large N gauge theory on a compact space with an external magnetic field

The phase structure of flavoured N=2 SYM on a three sphere in an external magnetic field is studied. The pairing effect of the magnetic field competes with the dissociating effect of the Casimir free energy, leading to an interesting phase structure of confined and deconfined phases separated by a critical curve of a first order quantum phase transition. At vanishing magnetic field the phase transition is of a third order. For sufficiently strong magnetic field, the only stable phase is the confined phase and magnetic catalysis of chiral symmetry breaking is realized. The meson spectra of the theory exhibit Zeeman splitting and level crossing and feature a finite jump at the phase transition between the confined and deconfined phases. At strong magnetic field the ground state has a massless mode corresponding to the Goldstone boson associated with the spontaneously broken U(1) R-symmetry analogous to the eta' meson in QCD.

Geodesics in information geometry: Classical and quantum phase transitions

We study geodesics on the parameter manifold for systems exhibiting second order classical and quantum phase transitions. The coupled nonlinear geodesic equations are solved numerically for a variety of models which show such phase transitions in the thermodynamic limit. It is established that both in the classical as well as in the quantum cases, geodesics are confined to a single phase and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.

Gate-controlled transitions in triple dots with interdot repulsion and magnetic field

We study the quantum phase transition (QPT) and electronic transport in triple quantum dots for a wide range of the gate voltage ϵ. We focus on the effect of the interdot repulsion V and the magnetic field B. In the case of particle–hole (p–h) symmetry and B = 0, we find the local quadruplet–doublet transition of first order when V increases to a critical point Vc ≈ U, where U is the on-site repulsion. Beyond the p–h symmetry, the sequence of the QPTs depends on ϵ. For small ϵ, a first order doublet–singlet transition is observed. For middle ϵ, we find the quadruplet–triplet transition of first order at Vc1 and the triplet–singlet transition of the Kosterlitz–Thouless type at Vc2. For large ϵ, there are two kinds of first order QPT with phase sequence quadruplet–triplet–doublet. The magnetic field B compensates for the effect of V. For V > U, as B increases we find a first order or second order QPT from a low-spin state to a high-spin state. The restoring of the Kondo effect and a perfect spin filtering is realized in the appropriate regime of the magnetic field.

Quantum phase transition in Bose-Fermi mixtures

We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero temperature. Within a quantum field theoretical model a two-step Gaussian approximation allows to capture the main features of the quantum phase diagram. We show that a repulsive boson-boson interaction is necessary for thermodynamic stability. The quantum phase diagram is mapped in chemical potential and density space, and both first and second order quantum phase transitions are found. We discuss typical characteristics of the first order transition, such as hysteresis or a droplet formation of the condensate which may be searched for experimentally.

Richardson-Gaudin models: the hyperbolic family

We show that the hyperbolic family of Richardson-Gaudin models could describe p-wave superfluids in two dimensional lattices. The analysis of the exact solution reveals an exotic phase diagram with a third order quantum phase transition. Moreover, we propose a separable integrable pairing Hamiltonian within the same family that could be useful to describe exactly superconductivity in heavy nuclei.

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

Through the Jordan—Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called “spin waves”, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.

Quantum criticality in inter-band superconductors

In fermionic systems with different types of quasi-particles, attractive interactionscan give rise to exotic superconducting states, such as pair density wave (PDW)superconductivity and breached pairing. In recent years the search for these newtypes of ground states in cold atoms and in metallic systems has been intense. Inthe case of metals the different quasi-particles may be the up and down spinbands in an external magnetic field or bands arising from distinct atomic orbitalsthat coexist at a common Fermi surface. These systems present a complex phasediagram as a function of the difference between the Fermi wavevectors of thedifferent bands. This can be controlled by external means, varying the density in thetwo-component cold atom system or, in a metal, by applying an external magnetic field orpressure. Here we study the zero temperature instability of the normal system as theFermi wavevector mismatch of the quasi-particles (bands) is reduced and find asecond order quantum phase transition to a PDW superconducting state. From thenature of the quantum critical fluctuations close to the superconducting quantumcritical point (SQCP), we obtain its dynamic critical exponent. It turns out to bez = 2 and this allows us to fully characterize the SQCP for dimensionsd ≥ 2.

Spontaneous symmetry breaking in a generalized orbital compass model

We introduce a generalized two-dimensional orbital compass model, which interpolates continuously from the classical Ising model to the orbital compass model with frustrated quantum interactions, and investigate it using the multiscale entanglement renormalization ansatz (MERA). The results demonstrate that increasing frustration of exchange interactions triggers a second order quantum phase transition to a degenerate symmetry broken state which minimizes one of the interactions in the orbital compass model. Using boson expansion within the spin-wave theory we unravel the physical mechanism of the symmetry breaking transition as promoted by weak quantum fluctuations and explain why this transition occurs only surprisingly close to the maximally frustrated interactions of the orbital compass model. The spin waves remain gapful at the critical point, and both the boson expansion and MERA do not find any algebraically decaying spin-spin correlations in the critical ground state.