## What is/are Random Singlet?

Random Singlet - We consider random singlet phases of spin1 2 , random, antiferromagnetic spin chains, in which the universal leading-order divergence ln 2 3 ln l of the average entanglement entropy of a block of l spins, as well as the closely related leading term 2 3 l in the distribution of singlet lengths are well known by the strong-disorder renormalization group (SDRG) method.^{[1]}The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

^{[2]}As an example, we show how the system can realize the so-called "random singlet phase", in which all atoms pair into entangled singlets, but the pairing occurs over a distribution of ranges as opposed to nearest neighbors.

^{[3]}Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this {\it frustrated\/} random singlet state.

^{[4]}We present here the evidences of a glass-like random singlet magnetic state in 1T-TaS2 at low temperatures through a study of temperature and time dependence of magnetization.

^{[5]}At maximum disorder our data indicate that this state may be identified with the theoretically predicted random singlet (RS) state.

^{[6]}Two-dimensional magnetic insulators exhibit a plethora of competing ground states, such as ordered (anti)ferromagnets, exotic quantum spin liquid states with topological order and anyonic excitations, and random singlet phases emerging in highly disordered frustrated magnets.

^{[7]}Entanglement features of the ground state of disordered quantum matter are often captured by an infinite randomness fixed point that, for a variety of models, is the random singlet phase.

^{[8]}

## random singlet phase

We consider random singlet phases of spin1 2 , random, antiferromagnetic spin chains, in which the universal leading-order divergence ln 2 3 ln l of the average entanglement entropy of a block of l spins, as well as the closely related leading term 2 3 l in the distribution of singlet lengths are well known by the strong-disorder renormalization group (SDRG) method.^{[1]}The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

^{[2]}As an example, we show how the system can realize the so-called "random singlet phase", in which all atoms pair into entangled singlets, but the pairing occurs over a distribution of ranges as opposed to nearest neighbors.

^{[3]}Two-dimensional magnetic insulators exhibit a plethora of competing ground states, such as ordered (anti)ferromagnets, exotic quantum spin liquid states with topological order and anyonic excitations, and random singlet phases emerging in highly disordered frustrated magnets.

^{[4]}Entanglement features of the ground state of disordered quantum matter are often captured by an infinite randomness fixed point that, for a variety of models, is the random singlet phase.

^{[5]}