Finite-scale emergence of 2+1D supersymmetry at first-order quantum phase transition

Abstract

Supersymmetry, a symmetry between fermions and bosons, provides a promising extension of the standard model but is still lack of experimental evidence. Recently, the interest in supersymmetry arises in the condensed matter community owing to its potential emergence at the continuous quantum phase transition. In this work, we demonstrate that 2+1D supersymmetry, relating massive Majorana and Ising fields, might emerge at the first-order quantum phase transition of the Ising magnetization by tuning a single parameter. Although the emergence of the SUSY is only allowed in a finite range of scales due to the existence of relevant masses, the scale range can be large when the masses before scaling are small. We show that the emergence of supersymmetry is accompanied by a topological phase transition for the Majorana field, where its non-zero mass changes the sign but keeps the magnitude. An experimental realization of this scenario is proposed using the surface state of a 3+1D time-reversal invariant topological superconductor with surface magnetic doping.

Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet

“…A close look at our numerical data tells us that the first-order transition exhibits an emergent SO(5) symmetry which was proposed in one variant of the DQC theory [82]. Emergent symmetry would not in general be expected at a first-order transition [70,83], but recently other examples have been found [65,84,85] where the coexistence state appears to be described by a vector or pseudovector combining all the components of the two different order parameters and transforming under a spherical symmetry. In the case at hand here the combined order parameter comprises three AFM components and two VBS components.…”

“…The tunneling barrier is absent if the order parameters form an enlarged spherical symmetry at the transition point, so that moving from one phase to the other corresponds to rotating the order parameter without energy cost. Such an unexpected mechanism at play at a first-order quantum phase transition was recently proposed to explain results for the transition between the AFM state and a twofold degenerate PVBS in the CBJQ model [65], and subsequently other potential cases were also identified [84,85].…”

“…Both of these scenarios were discussed in the context of first-order transitions with apparent O(4) symmetry in systems with AFM-PVBS transitions where the PVBS state is only twofold degenerate [65,84]. While an exact emergent symmetry at a first-order transition would be outside previous expectations, this scenario has some support also in a recent work claiming exact emergent supersymmetry at certain phase transitions with fermionic and bosonic degrees of freedom [85]. Here we do not provide any definite conclusions on the root causes of these unusual first-order transitions, but we address related issues using illuminating computational results.…”

“…While until recently emergent symmetries had only been expected at continuous transitions [70,83], subsequently a first-order transition with enhanced symmetry was also found in a Z 2 deformed classical 3D loop model [84]. It is currently not clear whether the enhanced symmetry is only manifested up to some large length scale or truly is asymptotically exact, but a theory in a different context of boson-fermion supersymmetry does suggest that first-order transitions can be associated with exact emergent symmetry [85]. Here we will demonstrate SO(5) symmetry at the first-order AFM-PVBS transition of the J-Q 6 model, thus providing yet another example of the emergence of enhanced symmetries under unexpected conditions.…”

Dual dynamic scaling in deconfined quantum criticality

“…In contrast, many critical systems show higher symmetry in the infrared limit than they do in the ultraviolet limit. For instance, spacetime supersymmetry can emerge at the critical point in some topological materials [3][4][5][6][7][8][9][10][11][12][13][14]; Lorentz symmetry can emerge in the superfluid-Mott insulator quantum phase transition [15,16], critical twosubband quantum wires [17], and phase transitions in Dirac systems [18][19][20]; SU(3) symmetry can emerge in the critical spin-2 chain with translational invariant interaction and in the critical spin-1 chain with random bond interaction [21,22]; extended O(N ) symmetry can emerge at the multicritical point [23][24][25][26]. In twodimensional (2D) spin systems, a prominent example in which the emergent symmetry arises as its characteristic phenomenon is the deconfined quantum critical point (DQCP) [27][28][29].…”