Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches

Baptiste, Bermond,; Chernodub, M. N.; Grushin, Adolfo G.; Carpentier, David

doi:10.48550/arxiv.2206.08784

Cited by 4 publications

(7 citation statements)

References 83 publications

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“…4 To put it simple, ϕ µ ν is the Hodge dual of the equations of motion for Ω µ ν . 5 In addition to the 3 + 1 decomposition of the Lagrange multipliers and auxiliary fields we also need to introduce the 3 + 1 decomposition of the curvature, torsion and non-metricity into the action S in (7). The full details of the derivation are given in section 4.…”

Section: Geometric Setup and Summary Of The Main Resultsmentioning

confidence: 99%

“…In most cases, the spacetime metric is the only dynamical field associated to the geometry, while further geometric structures are argued to be irrelevant by appealing to current experimental evidence. Recently, however, general spacetimes with non-vanishing curvature 1 Ω µ ν and torsion T µ found applications in condensed matter systems-where lattice deformations generate non-trivial Ω µ ν and T µ directly coupled to the electronic degrees of freedom-as a means to simulate high-energy phenomena in tabletop experiments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In particular, torsion has been shown to alter the the hydrodynamic expansion by introducing terms relevant for both heavy-ion physics and electron flows in condensed matter [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

et al. 2023

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Motivated by establishing holographic renormalization for gravitational theories with non-metricity and torsion, we present a new and efficient general method for calculating Gibbons-Hawking-York (GHY) terms. Our method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in (n-1)+1(n−1)+1 dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes’ theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for torsionful Lovelock-Chern-Simons and metric-affine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within AdS/CFT.

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Section: Geometric Setup and Summary Of The Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

et al. 2023

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“…The Floquet unitary evolution is generated by spatially deformed Hamiltonians, as studied extensively in recent works on Floquet CFTs [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. There are dynamically generated hot spots serving as the reservoir, which are depicted as the black dots (heating regions) in Fig.…”

Section: Heating Regionmentioning

confidence: 99%

Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems

Wen¹,

Fan²,

Vishwanath³

2022

Preprint

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We propose a general method of cooling-periodic driving generated by spatially deformed Hamiltonians-and study it in general one-dimensional quantum critical systems described by a conformal field theory. Our protocol is able to efficiently cool a finite-temperature Gibbs (mixed) state down to zero temperature at prescribed sub-regions exponentially rapidly in Floquet time cycles. At the same time, entropy and energy are transferred and localized to the complementary regions that shrink with time. We derive these conclusions through an exact analytic solution of the full time evolution of reduced density matrices. We also use numerics in free-fermion lattice models as a benchmark and find remarkable agreement. Such conformal Floquet refrigerators open a promising new route to cooling synthetic quantum systems.

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“…Here, it is left undetermined, so that the reader may adapt this to his favorite conventions. For primaries, correlators at finite temperature can easily be obtained from ( 22) by using the transformation (13) together with the thermalizing conformal transformation (16). This yields…”

Section: Correlatorsmentioning

confidence: 99%

“…Indeed the free energy of quantum critical systems [11,12] was discussed in the context of the conformal anomaly, however those works focus on the appearance of the conformal anomaly in thermal properties such as specific heat [12] and thermal conductivity [13]. In addition, thermal effects for curved space were connected to the conformal anomaly in [14][15][16], which are difficult to observe in experiments. Altogether, to date there exist no predictions on how the conformal anomaly is manifested in spin observables.…”

mentioning

confidence: 99%

Conformal anomaly in magnetic finite temperature response of strongly interacting one-dimensional spin systems

Northe¹,

Zhang²,

Wawrzyńczak³

et al. 2022

Preprint

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The conformal anomaly indicates the breaking of conformal symmetry (angle-preserving transformations) in the quantum theory by quantum fluctuations and is a close cousin of the gravitational anomaly. We show, for the first time, that the conformal anomaly controls the variance of the local magnetization M loc at finite temperatures in spin chains and spin ladders. This effect is perceived at constant and variable temperature across the sample. The change of M loc induced by the conformal anomaly is of the order of 3-5% of the maximal spin at one Kelvin for DIMPY or CuPzN and increases linearly with temperature. Further, for a temperature gradient of 10% across the sample, the time-relaxation of the non-equilibrium M loc is of the order of nanoseconds. Thus, we believe that experimental techniques such as neutron scattering, nuclear magnetic resonance (NMR), spin noise and ultrafast laser pumping should pinpoint the presence of the conformal anomaly. Therefore, we pave the road to detect the conformal anomaly in spin observables of strongly interacting low-dimensional magnets.

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Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches

Cited by 4 publications

References 83 publications

Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems

Conformal anomaly in magnetic finite temperature response of strongly interacting one-dimensional spin systems

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