No abstract

We consider a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. A possible example is the recently proposed many-body localization transition, in which transport coefficients vanish at a critical temperature. Describing this unconventional quantum criticality has been technically challenging as understanding the finite-temperature dynamics requires the knowledge of a large number of many-body eigenstates. Here we develop a real-space renormalization group method for excited state (RSRG-X), that allow us to overcome this challenge, and establish the existence and universal properties of such temperature-tuned dynamical phase transitions. We characterize a specific example: the 1D disordered transverse field Ising model with interactions. Using RSRG-X, we find a finite-temperature transition, between two localized phases, characterized by non-analyticities of the dynamic spin correlation function and the low frequency heat conductivity. arXiv:1307.3253v3 [cond-mat.str-el]

Spontaneous symmetry breaking plays a key role in our understanding of nature. In a relativistic field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitations: massless Nambu-Goldstone modes and a massive 'Higgs' amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particles [1] and also appears as a fundamental collective mode in quantum many-body systems [2]. Whether such a mode exists in low-dimensional systems as a resonance-like feature or becomes over-damped through coupling to Nambu-Goldstone modes has been a subject of theoretical debate [2][3][4][5][6][7]. Here we experimentally reveal and study a Higgs mode in a two-dimensional neutral superfluid close to the transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected softening of the onset of spectral response when approaching the quantum critical point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum-field [2,8,9], constituting a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations, which also addresses the consequences of reduced dimensionality and confinement of the system. Our work constitutes a first step in exploring emergent relativistic models with ultracold atomic gases.Higgs modes are amplitude oscillations of a quantum field and appear as collective excitations in quantum many-body systems as a consequence of spontaneous breaking of a continuous symmetry. Close to a quantum critical point, the low-energy physics of such systems is in many cases captured by an effective Lorentz invariant critical theory [2]. The minimal version of such a theory describes the dynamics of a complex order parameter Ψ = |Ψ|e iφ near a quantum phase transition between an ordered (|Ψ| > 0) and a disordered phase (|Ψ| = 0). Within the ordered phase, the classical energy density has the shape of a Mexican hat (Fig. 1a) and the order parameter takes on a non-zero value in the minimum of this potential. Hereby, its phase φ acquires a definite value through spontaneous breaking of the rotation symmetry (i.e., U (1) symmetry). Expanding the field around the symmetry broken ground state leads to two types of modes: a Nambu-Goldstone mode and a Higgs mode related to phase and amplitude variations of Ψ, respectively (Fig. 1a). In contrast to the phase mode, the amplitude mode has a finite excitation gap (i.e., a finite mass), which is expected to show a characteristic softening when approaching the disordered phase (Fig. 1a). The sketched minimal model of an order parameter with N = 2 components belongs to a class of O(N ) relativistic * Electronic address: manuel.endres@mpq.mpg.de field t...