Dynamical Response near Quantum Critical Points

Lucas, Andrew; Gazit, Snir; Podolsky, Daniel K.; Witczak-Krempa, William

doi:10.1103/physrevlett.118.056601

Cited by 27 publications

(47 citation statements)

References 42 publications

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“…Our holographic computation reveals that, independent of the details of the ground state, the asymptotics of the response functions are given by (1.3), with all coefficients in the expansion determined completely by the UV CFT. We expect that -with some important exceptions in broken symmetry phases [20] -this is a robust result of our analysis, valid beyond the large-N limit.…”

Section: Jhep07(2017)149supporting

confidence: 67%

“…In this paper, we will discuss the asymptotics of a variety of response functions at high frequency [5,8,[11][12][13][14][15][16][17][18][19][20]. We will show that in holographic field theories, this asymptotics is universal and does not depend in any detailed fashion on the nature of the ground state.…”

Section: Jhep07(2017)149mentioning

confidence: 97%

“…It can fail in regions separated from the quantum critical "fan" by a phase transition, where potentially new gapless modes can arise. An example of this failure was shown in the broken symmetry (Goldstone) phase in the vicinity of the Wilson-Fisher O(N ) QCP at large N [20]. The leading order coefficient C X X is an operator normalization in the vacuum of the CFT.…”

Section: Jhep07(2017)149mentioning

confidence: 99%

“…We will present two derivations of (1.3): one using conformal perturbation theory applied to general CFTs (such an approached was succinctly presented for the conductivity in [20]), one using holography. We will show that these approaches exactly agree.…”

Section: Jhep07(2017)149mentioning

confidence: 99%

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Quantum critical response: from conformal perturbation theory to holography

Lucas¹,

Sierens²,

Witczak-Krempa³

2017

J. High Energ. Phys.

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We discuss dynamical response functions near quantum critical points, allowing for both a finite temperature and detuning by a relevant operator. When the quantum critical point is described by a conformal field theory (CFT), conformal perturbation theory and the operator product expansion can be used to fix the first few leading terms at high frequencies. Knowledge of the high frequency response allows us then to derive nonperturbative sum rules. We show, via explicit computations, how holography recovers the general results of conformal field theory, and the associated sum rules, for any holographic field theory with a conformal UV completion -regardless of any possible new ordering and/or scaling physics in the IR. We numerically obtain holographic response functions at all frequencies, allowing us to probe the breakdown of the asymptotic high-frequency regime. Finally, we show that high frequency response functions in holographic Lifshitz theories are quite similar to their conformal counterparts, even though they are not strongly constrained by symmetry.

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Section: Jhep07(2017)149supporting

confidence: 67%

Section: Jhep07(2017)149mentioning

confidence: 97%

Section: Jhep07(2017)149mentioning

confidence: 99%

Section: Jhep07(2017)149mentioning

confidence: 99%

See 2 more Smart Citations

Quantum critical response: from conformal perturbation theory to holography

Lucas¹,

Sierens²,

Witczak-Krempa³

2017

J. High Energ. Phys.

Self Cite

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show abstract

“…However, this phenomenon has been far less studied in other types of systems. Many studies have examined simpler systems, such as models described by relativistic conformal field theories having z = 1, which enjoy additional symmetries that constrain the dynamics [3,7,8].In this work, we reveal multiple dynamical exponents in a new setting: a strongly correlated 1d spin system. Further, these exponents will be shown to vary continuously as a function of a coupling in the Hamiltonian.…”

mentioning

confidence: 78%

Quantum spin chains with multiple dynamics

2017

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Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale DMRG simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤ z < 2.7, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wavefunction for the groundstate, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the non-equilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in 2d.It is common for many-body quantum systems to possess multiple time-scales that determine the low-energy dynamics. In a gapless system, the dynamics will be characterized by the dispersion relation of the excited states (quasiparticles need not exist), E = Ak z , where k is the wavevector of the mode and z the dynamical exponent. Different modes can have different z exponents. For instance, a metal near a quantum critical point can have different dispersions for the electrons and the various order parameter fluctuations [1][2][3][4][5][6]. However, this phenomenon has been far less studied in other types of systems. Many studies have examined simpler systems, such as models described by relativistic conformal field theories having z = 1, which enjoy additional symmetries that constrain the dynamics [3,7,8].In this work, we reveal multiple dynamical exponents in a new setting: a strongly correlated 1d spin system. Further, these exponents will be shown to vary continuously as a function of a coupling in the Hamiltonian. The spin 1 quantum spin chain in question is a generalization of the so-called Motzkin Hamiltonian introduced by Bravyi et al [9]. Its groundstate can be determined exactly but not its excitation spectrum. With the help of large-scale Density Matrix Renormalization Group (DMRG) simulations, we discover low lying excitations with different dynamical exponents. In order to gain insight in the low-lying spectrum we determine a continuum version of the groundstate, and find a parent Hamiltonian. The latter possesses an excitation spectrum that is distinct from the spin chain but can provide useful insight into the construction of the full low energy field theory. This illustrates how a given groundstate can have starkly different excitations, and offers some g...

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Conformal correlators as simplex integrals in momentum space

Bzowski

McFadden

Skenderis

2021

J. High Energ. Phys.

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We find the general solution of the conformal Ward identities for scalar n-point functions in momentum space and in general dimension. The solution is given in terms of integrals over (n − 1)-simplices in momentum space. The n operators are inserted at the n vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentum-space cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where n-point functions are built in terms of (n − 1)-point functions. To illustrate our discussion, we derive the simplex representation of n-point contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the star-mesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves (n − 2) integrations, which is an improvement (when n > 4) relative to the Mellin representation that involves n(n − 3)/2 integrations.

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Dynamical Response near Quantum Critical Points

Cited by 27 publications

References 42 publications

Quantum critical response: from conformal perturbation theory to holography

Quantum critical response: from conformal perturbation theory to holography

Quantum spin chains with multiple dynamics

Conformal correlators as simplex integrals in momentum space

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